The Allegory of the Cave and Open Your Eyes are thematically tied together through the idea of perception and reality and how they relate to one another. One could experiment with the idea that Cesar could be considered a prisoner of the cave in his daily life, but Nuria was the catalyst that unchained Cesar from the wall, and that the average normal life Cesar knows is in fact an illusion. After his accident Cesar sees things beyond his ‘normal’ life that he was unable to see before. After his run into Sofia and Pelayo and he awakens on the street that is when Cesar becomes confused as to what is reality and what is Cesar’s “artificial perception” of life. The confusion between the two worlds would seem to be Cesar’s escape from the cave, the difference between what he thought he knew to be real and what in fact would be considered ‘reality’.
Cesar’s mind obviously has capabilities beyond what it had been before the accident. You see Cesar perceptions of Sofia and Nuria being the same person, or any of the other surreal happenings, could have been created in Cesar’s mind after his disfigurement or it this instances could be Cesar just seeing a new truth. It could be interesting to think of ‘reality’ as the thing that is holding Cesar back in ignorance in some ways, and “artificial perception” could be just as real in Cesar’s mind. Once Cesar perceived something, real or imagined, it became a real experience that he had even if it wasn’t part of reality. This tear in Cesar’s mind between the imagined and the real is very similar to trying to adjust to a new reality.
At the end of the film Cesar is trying to find his way back to a reality, but it can never be the life he had before no matter how badly he wants that. Is Cesar insane? Did everything Cesar experience happen? Cesar jumps off the roof in an attempt to finally open his eyes to world outside the cave he had been living in. Cesar does not know what in his life has been real and what in his life has been artificial. The audience is able to experience all of Cesar’s pain in learning and experience the new way that he sees life to be, and he decides to go through the pain of jumping off a building in order to find a new bigger truth.
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Intro to Philosophy of Film 
I find your way of connecting the film and Socrate’s idea very interesting: the artificial perception in Cesar’s mind is the cave. Although Cesar has absolute control of the virtual reality, he has limited knowledge about that. Therefore what he perceived is only appearance. However, I do not agree with the idea that Nuria helps Cesar to escape from the cave. Cesar escapes because he starts to question about the world he lived and wants to solve the puzzles he had all the time after he sees the chief executive of Life Extension on TV. Therefore, Nuria is just one of the appearances to Cesar while the doubts that Cesar has actually help him unlock the chains. This idea of questioning is consistent with Socrate’s way of discovering the truth. Therefore, Cesar’s choice of leaving the virtual reality at the end of the film becomes evident because a person, who knows the truth, would feel sorry for those innocent people and try to save them. Cesar saves himself at the end of the film.
I agree you in that the juxtaposition of The Allegory of the Cave and Open Your Eyes definitely challenges our perception of what is real and what is not. It makes us wonder if we are actually “awake” right now. If you can only realize that you were dreaming after you woke up, how would you know if you are not reading this in your dream right now? Your point also makes me wonder if it is possible that our known “waking” state is really a dream while our dream is really a peak into reality. However, I do have to point out that the confusion, you mentioned, between Cesar’s two worlds is not exactly his escape from the cave but really what prompted him to question his surroundings. It is the questioning that ultimately lead him out of his dream.
Answering the questions in your last paragraph, I don’t think Cesar is too crazy for wanting his old life, the one with possibility of Sophia. It is quite naturally of him to yearn for that. However, we see a change in him by the end of the movie. Instead of hopeless chasing something that we will never get, Cesar has matured and decided to chase something real. Even though he knows that Sophia is not going to be there when he wakes up in reality, he still chooses reality because he wants what is tangible and actually plausible. This final act of his says a lot about his mental strength.