There are probably 25 reasonable candidates for the best movie ever made, it all depends on your tastes. But three of those candidates circle each other in interesting ways.

Federico Fellini’s 1963 film “8 1/2” is a movie about making a movie, but even more than that, it’s a deep examination of Fellini’s psyche. Fellini suffered from bouts of depression throughout his life and had been in Jungian analysis for a few years before starting this film. He was blocked, not knowing what to do for his next film after rewriting the language of Italian cinema with “La Dolce Vita.”

So he made the process of not-knowing what to do next the subject of his film and ended up inventing a code phrase “asa nisi masa” that opens up explorations within the film about the protagonist Guido’s relationships with women. The phrase is commonly decoded as a pig latin variation of anima. So Fellini was applying his Jungian analysis to all of the anima figures in his life — and oh my God, did he have an army of them.

What’s fascinating about “8 1/2” is that the protagonist Guido fails in his quest to make the movie within the movie, but Fellini conquers his alter ego by not only finishing his film, but making one that’s incredibly coherent for something so fractured and dreamlike — and completing a work that’s widely regarded as a masterpiece. So Fellini, in essence, conquered his primal fears. But by doing so, he made a movie that succeeded so completely that he placed himself permanently in Guido’s position — he will make many more films his in career, but none will come close to the genius of “8 1/2.”

Another candidate for that greatest film title is Ingmar Bergman’s 1965 film “Persona.” Right before making this film, Bergman made a bizarre farce (in color — his first color film) called “All These Women.” It was basically a ripoff of “8 1/2” that didn’t work at all. Bergman then went into a deep depression and, like Fellini, jumped into a project that became too unwieldy to complete.

So instead, he made his own hall of mirrors film, “Persona.” Unlike Fellini’s masterwork, there is no obvious Bergman alter ego in this film. Most of the film consists of two women — an actress and a nurse — alone on Faro Island in Sweden, trying to forge a relationship despite the fact that, after a panic attack on stage mid-performance, the actress ceased talking.

But to say this is what “Persona” is about is misleading — it’s also a film about making movies … or, perhaps more accurately, it is an anti-movie, with numerous devices thrown in to keep the audience at at distance and prevent them from being sucked in by the story telling and relating too deeply to any character or story.

Tarkovsky began to think about and then draft the screenplay for “Mirror” (along with his collaborator Aleksandr Misharin) in 1964, right after “8 1/2” and right before “Persona.” It underwent numerous revisions in detail and style over the next ten years. But there’s no question that the filmmakers were dreaming this movie up amidst a film revolution that included many more players than just Fellini and Bergman, but was heavily influenced by both.

So, as we transition out of Tarkovsky’s powerful anti-war segment of “Mirror,” we return to the family story. It begins with the father, the distant poet, returning briefly to the family while on leave during World War II. The movie then abruptly shifts to the 1960s with Alexi discussing his son Ignat with his ex wife — and another request that Ignat live with him.

This leads to Alexi directly asking Ignat if he wants to come live with him, and Ignat immediately rejects the idea, as if it’s absurd to even ask. This leads to an interesting little psychological play between Alexi and his ex wife — she keeps trying to bring up Alexi’s poor relationship with is mother while Alexi wants to change the subject to what a disappointment Ignat has become and how she is to blame for it.

The punchline to this family warfare is Alexi asserting that Ignat’s mediocre academic record (which he cruelly calls embarrassing to himself) might lead to him being drafted, but that might be good for him. After experiencing all we have just observed about war in the film, it’s impossible to take this statement at face value. In fact, it all feels like Alexi being stung by Ignat’s refusal to move in with him, so he degrades his son instead.

This is psychologically rich material — in some ways deeper than anything Fellini or Bergman supplied in their more overtly self analytical films. What makes Tarkovsky’s insights stand out is that he steers clear of psychoanalytic terms and well defined tropes and sticks to the ways pathologies are passed down through families … and also alludes to how religions and countries play into these pathologies defining populations over time.

Tarkovsky is attempting something at the scale of Tolstoy — even as he keeps reminding us that the story is essentially just about his mother. It is in a sense … but it’s also about mother Russia.