In the Universe/Franchise of Saint Seiya what can be considered Canonical and Non-Canonical in the Galaxian Myth.
Saint Seiya (Classic Manga) & Saint Seiya: Next Dimension
This is the simplest thing to explain, and what should be by far the most obvious. Needless to say, the Classic Manga is canonical, as it is the original storyline which gave birth to the franchise that is known today.
Saint Seiya: Next Dimension is also canonical as it is the Classic Manga's direct sequel, as was directly stated in Vol. 1:
Over 240 Years before the confront of Seiya and Hades at Elysion, the passionate bonds of friendship of two youths are separated, another Holy War is about to begin!! Past and present intertwine in a new Galaxian Myth, the legitimate sequel of Saint Seiya is about to begin!!.
Saint Seiya: Episode G & Episode G: Assassin
By far the most controversial of all Saint Seiya series, Episode G is an installment whose canonicity has been debated ever since its inception. Here I will attempt to demonstrate all sources that state it's status as either canon or non-canon:
In a Interview at Champion Red No.1, 2003, Masami Kurumada explains his intentions with the release of Episode G:
Q: Saint Seiya Episode G arrived as a true surprise. Why are you starting Episode G now?
Kurumada: My answer shall be the same as the one George Lucas has given in regards to the production of his Stars Wars Episode I. A conductive environment to the materialization of what I already imagined has simply arrived. With the context of a film, this refers to digital imaginary and new technologies, for a manga it means the new circumstances of the environment.
So Masami Kurumada's intentions with the creation of Episode G was to make a prequel, akin to Star Wars's The Phantom Menace. Not a non-canon Spin-Off.
Continuing, in December of 2003 Masami Kurumada had an interview with the French Magazine Anime Land #97, where he talked about Episode G:
AL: Besides the series Ring ni Kakero 2, which you write and draw yourself, in 2002 you brought us the beginning of Saint Seiya Episode G, drawn by Megumu Okada, and also the new saga of Fuma no Kojira, drawn by your direct disciple Satoshi Yuri. Can you tell us more about these projects? MK: I develop a supervision over them, however the artists are totally free to develop the plot. Megumu Okada has made a trully impressive work, but he prints on it his own style and story. Satoshi Yuri is very responsible and works very seriously. He is my student, we work on the same studio, therefore I can take more of my time with his work than with Episode G.
So Masami Kurumada supervises mangas based on his original work, and the only reason he didn't dedicate more time to Episode G was that he was handling multiple manga.
An official Saint Seiya website lists Masami Kurumada as being directly involved in the creation of Episode G:
Original Draft by Masami Kurumada, Drawings by Megumu Okada.
And as one last proof:
The website that publishes the Episode G: Assassin Webcomic describes it as:
The legendary super hit series "Saint Seiya" dominates the world with a new legitimate gaiden!
In both the previously posted Next Dimension Scan and the above line, the japanese word 正統 (Seitō) is mentioned, and it means Orthodox / Legitimate, in this case stating that something is original/canon.
Saint Seiya Episode G and Episode G Assassin are absolutely Canon for the Franchise / Universe of Saint Seiya.
Saint Seiya: Saintia Shō
Saintia Sho is, by comparison with Episode G, far easier to explain. Two interviews give explicit evidence regarding it's canonical status. The first one is Chimaki Kuori's interview with the French Magazine La Monde, at Japan Expo 2016:
Le Monde: What was your main challenge in the creation of a feminine series about "Saint Seiya", a primarily masculine universe?
Chimaki Kuori: The decision of accepting it was already certain. It meant launching myself into an exhaustive work, and facing the critical eyes of fans used to a canonical universe extremely known and appreciated, without being sure of how they'd receive this reinterpretation. (...) Obviously the male characters reappear, because the series takes place in the same world as the original.
Chimaki Kuori also answered live questions at the place, and while there was no filming, a french Saint Seiya fan named Guillaume Boutet wrote a summary on it:
They then asked her about the manga's creation process, about its relation with Kurumada and the difficulty of writing a story supposedly parallel to the original. Chimaki then remembered Kurumada's own words: "If the story is good, you can accept and ignore some things. The important is to have a good rhythm and for you to have enjoyment in reading the series." She tells that, in the beginning of the project, the idea of focusing on women serving Athena came from Kurumada, some years ago when he was hospitalized. It took some years for the idea to mature, and when Chimaki Kuori was contact, he gave her a general draft to follow, with no duration or number of volumes programmed. If she could finish the progressing story, he'd already be happy.
About the enchange of ideas with Kurumada, Chimaki Kuori reveals that with every new story arc she would send him the script, who would read it all. Kurumada gave her relative freedom, dedicating himself specially in controlling that the series would maintain the "Saint Seiya" spirit. When a fan asked her if she followed the anime or manga to create Saintia Sho, she answered that she greatly enjoyed the anime, but that it had already tried everything. From the anime film, came Eris, the Goddess of Discord, and her becoming the antagonist of Saintia Sho. Chimaki Kuori said that she "pretended the movie to have never happened". The choice of Eris was done by Kurumada, just like the idea of making the story's cast as feminine as possible, and a lot became related to the anime movie because it was the film with which Kurumada had been involved the most at the time.
So, it's very, explicitly obvious that Saintia Sho is set within the Classic Manga's world, functioning as a parallel story, and that the project derives from Masami Kurumada himself, who is greatly involved in the creative process as a supervisor. I can safely consider it canon as well.
Saint Seiya: Lost Canvas
Of all the Saint Seiya Spin-Offs, Lost Canvas is the one most often considered Non-Canon by the fanbase. After all, it takes place within the same time period of the declared canon Next Dimension, and both manga are completely different and contradictory. Naturally the Spin-Off would be excluded from continuity. Correct? Yes and no.
Firstly, Saint Seiya: Lost Canvas absolutely does not take place within the same chronology as the Classic Manga, Next Dimension, Episode G and Saintia Sho.
Do you remember the statement that Next Dimension is canonical? That was released with the publication of the manga's Vol.01, released on February 06, 2009. When Lost Canvas was announced back in August 17 2006, mere weeks after Next Dimension's beginning on April 26, it was with this message:
Preview of urgent announcement! Another creation of Seiya...! "Saint Seiya The Lost Canvas Meiou Shinwa"
From NEXT DIMENSION to THE LOST CANVAS,
Kurumada's DNA is now passed to here!!!
Creation: Masami Kurumada
Manga: Shiori Teshirogi A new series!
For the first time in history, a "Multi-Angle-Dual" series, with two Cosmos from two angles a "Myth of Hades" (Meiou Shinwa) is drawn!!
Originally, both Next Dimension and Lost Canvas were sold as two different, yet equally valid interpretations of the same story.
The closest any source has ever come to calling it "Non-Canonical" was the Princess Gold Magazine, which said this:
A popular work in the form of Another Story expands, while at the same time sharing concepts [With Next Dimension]
Finally, there is this Interview with Shiori Teshirogi for the French Website Unificationfrance
Did Saint Seiya have a particular impact in your career?
Yes, but aside from Saint Seiya, all works from Masami Kurumada influenced my career.
How did you arrive at The Lost Canvas?
A long time ago, I went to an autograph session of Masami Kurumada. When I met him, I gave him one of my already published manga and said: "I became a professional artist thanks to you who influenced my career." I thought things would end there, but years after he made contact with me saying he had read my manga. He found them excellent and offered me to write his new Saint Seiya manga. And that's how it went. It was really extraordinary.
Masami Kurumada was personally involved in writing The Lost Canvas
When Lost Canvas began he just gave me a list of key scenes and events to follow with the plot, and told to use them as basis for my own script. As Lost Canvas lasted more than expected, I ended up quickly finishing this list, and so Kurumada-Sensei told me "There's no problem Teshi, I'll let you do whatever you want from now on. You have total freedom."
This confirms that The Lost Canvas, much like other manga in the Franchise, are projects coming from Masami Kurumada himself. Rather than completely separate, Non-Canonical works. The Lost Canvas could be considered as a parallel universe in the franchise of Saint Seiya.
Comment by Masami Kurumada
Next Dimension Vol.06
As a last note, I will share Masami Kurumada's own words at the publishing of Next Dimension Vol.06:
For a long time Kurumada's works have been adapted through various communication medias and different Spin-Offs. However, sometimes I hear opinions like "This isn't like the original work". It's certain that each derivative media is influenced by the artists or producers that find themselves in charge, and is possible that their content differs greatly from the original manga. Regardless, they are nothing more than a generation of children who grew appreciating Kurumada's works, and I know that the passion that passion that drives them into creating these derivatives is incomparable. And this is why with peace of mind, I can entrust these manga to them, as if they were my children. If Kurumada's Manga was a brand, then you could say that the other works are its derivatives and successors, and it is perhaps inevitable that they depart farther and farther away from the hand of the original creator.
Masami Kurumada is aware that he cannot hold Saint Seiya for long. He's old, his health isn't the greatest, and he cannot write and draw with under the same type of schedule he used to. And so he trusts his series into the hands of successors, so they'll carry on his brand. And so Saint Seiya stays alive, and in constant growth and renovation.
Saint Seiya Multiverse
The multiverse (or meta-universe) is the hypothetical set of possible universes, including the universe in which we live. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, and the physical laws and constants that describe them.
The various universes within the multiverse are called "parallel universes", "other universes", or "alternative universes".
In Next Dimension (chapter 75) appear two universes different from the main universe. Through the deformations in time-space that appeared in the Sanctuary. Shiryu travels to another world or parallel universe, where he lived and died as an ordinary person. And Tenma traveled to a another world or parallel universe, a world of darkness.
In The Lost Canvas also appear other universes different from the main universe.
- Gaiden Aries (chapter 77-78) appears a universe with a different future. In this future the Saints are defeated in the Holy War and Hades killed Athena. Aries Avenir and a group of Saints who survived to the Holy War, with the help of the Chronos, traveled back to the Holy War of the 18th century to change the future of the universe. The intervention of Aries Avenir in the past, created the timeline or main universe of the work of Saint Seiya The Lost Canvas.
- Gaiden Aries (chapter 78), Kairos, a minor god of time, mentions the existence of different parallel worlds.
- Gaiden Sagittarius (chapter 66), Phythia, an oracle, mentions that the universe does not have only one future, since there are different futures in the same universe. A universe branched into multiple futures or parallel universes like the branches of a tree.
In Episode G Assassin also appear other universes different from the main universe. In this manga is where the existence of the multiverse is explained, and its history is developed with the intervention of Saints from other universes.
The chapter 80 of Episode G Assassin confirms the existence of a multidimensional universe, also known as multiverse.
Dohko explains to Shiryu the existence of the multiverse:
"Different universes and worlds exist very close to each other within of the multiverse. It's just that none of them is able to perceive the border between the two."
This confirms that the different works of SS are part of a multiverse, therefore, all the mangas, animes, novels, etc. are part of the canonical multiverse of the Saint Seiya franchise.