Ok I have a separate theory that is a bit different from the others I have read online.
My problem with most interpretations is that they leave out Nemo’s ability to see the future (at least to a limited extent) and the importance of the big crunch event in the end. In my theory, these two circumstances creates a paradox, and in turn a very situational superhero, like in the case with Neo in the Matrix. I also dislike the idea of "it was all just a dream!" or "it was an imagination. Nothing happened and noone exists". It feels too cliché for the visual greatness of this movie. I know that there are a scene in the end, where the city is taken apart piece by piece and Nemo explains to the reporter that they do not exist outside of the architects mind, being the boy at the train station. While I do agree that the boy can serve as an architect in some sense, I do not want to take the rest of the dialog literally.
The paradox in mind is created as the young Nemo is faced with the impossible choice at the train station. I am aware that this does not make perfect scientific sense, but bear with me anyway. As Nemo is faced with the choice, he can see all the ways his life will turn out depending on which way he chooses. But, as the old Nemo declares in the end, this does not help him to make a desicion. The reason is, since none of Nemo’s timelines seem to be perfect, everyone one way or another ending in tragedy or a dissatisfactory state, he will, once knowing about the outcome, choose another alternative. But instead of the idea of a nonexsisting Nemo making it to the old age and remembering the many life paths, the old Nemo is a human Shrödinger’s cat. As no one in the futuristic world have any record of his existence, the man is the cat in the box, where every outcome is just as plausible and must be imagined as ‘true’. As the old Nemo has unclear and contradictory memories of his own life, he either have lived all of them, or has forgotten which is right, meaning that they all gain the same meaning.
Another thing is that Nemo has the power to communicate with himself through the different timelines. I do not fully understand the mechanics of the argyle reality, but apparently the knowledge of the big crunch, achieved by another version of Anna in the Mars timeline, is transferred from old nemo to a younger version some way through this world. This knowledge is of large importance for my theory and has not been covered by many other theories that I have seen. Knowing that Nemo has to stay alive until a certain time, in order to get “a second shot”, as Anna put it. It could very well be that the Argyle reality does not really exist, however. It could be a representation of a dream state, imaginary visualization by the boy at the train station, I do not know.
As the big crunch happens, time starts going backwards. At the deathbed, Nemo states that “this is the best day of my life”. His last words are “Anna”, who is the one his happy incarnations have been about all the time. The big crunch allows the possibility for Nemo not so much to relive his life, as to make his past life turn out in the most happy way. The old nemo may not know how his live really turned out, or rather, it turned out in every way. But given the fact of his many possibilities, due to the paradox, he can choose his beginning with knowledge of the best ending. When time goes backwards there will be no crossroads, no more decisions that has been his prison up to this point. All he has to do is to follow the thread in the opposite direction. This also solves the paradox, as suddenly there is only one way that he can have lived his life; backwards makes forwards. Note that this is only working for Nemo, as any other lives would already have its path staked out perfectly and no uncertainties about the timelines would exist. Notice how the nurses in the end scene are seemingly just played backwards while old Nemo chuckles happily.
A few flaws with my theory:
Out of logic reasons, one would suspect that he would have to make it till old age, and therefore, the timelines where he dies young would have to be discarded.
I am also aware that in a real life, the young Nemo would have to make one desicion at the train station; the option to not choose is never there. But while I am not a professor in quantum physics, I do believe that this depends on your point of view. While the young Nemo may have a choice, the elderly Nemo in a world where no one knows about his past could very well exist with the theoretical position that Nemo may never have made a choice, and that therefore, all options are possible. If not scientifically accurate, I would say it is very poetical. If nothing else, it gives me a good feeling to think of that Nemo gets the best life, the one where he meets Anna in the end.
As someone else noted: “Anna” is the same spelled backwards and forwards. There are more examples of this in the film.