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I also feel they are the same person, and the conceit of the film is that his duality is expressed through two lives. On a practical level, there's no way Anthony could support his lavish lifestyle with three bit parts in local movies. Also, the apartment with his girlfriend doesn't seem complete, as if its a makeshift home (Anthony even says to Adam, "You live like this?" or something to that effect). The man who recommends the movie "Where There's a Will, There's a Way" (an ironic title for this film's fatalism) is actually hinting to Adam that he recognized him in the film and knows about his secret life. When the girlfriend asks who he is after seeing the mark of his ring, it makes far more sense that she means it in a "I don't know you anymore" kind of way rather than instantly suspecting that a doppelganger is trying to molest her, only to allow him to drive her home minutes later. And, as it has been pointed out, his mother's reaction to his story and acknowledgement of his acting career pretty much cements this idea. So, the spiders... Adam and Anthony clearly have a fear of female sexuality and intimacy (which includes having a family); the spider strikes me as a projection of their mutual disgust of women, as I believe Swo mentioned. Adam attempts to have sex with his girlfriend while she is sleeping, and Anthony attempts to have sex with, uh, his girlfriend under false pretenses. Both situations are attempting to remove the interpersonal element from sex. The sex club is the ultimate expression of this hostility and alienation towards sexuality. Letting the spider loose at the beginning of the film is setting in motion a visual motif that indicates he has always been in a trap of his own making as he attempts to wrestle with these aspects of his identity. His attempt to control this issue (symbolized by the woman crushing a spider) will inevitably fail. We see it moseying its way towards the apartment near the end of the film before anything is settled, as the result is inevitable--after all, there are limited solutions when he is dealing with himself, especially in the film's hermetic environment. So, the first time it happens, it is a tragedy, but the second time it happens, which is to say, after he makes his way back to being emotionally available to his wife only to see the Unica key (a nod to Notorious), which suggests an easier option and starts a new (yet old) lie in order to explore it, then it becomes a farce. That's why the Walker Brothers song seems out of place, as if its trivializing the ending, because it is. History repeating is the pathetic farce of our fallible nature and finite possibilities.