A Perfect Circle:
I'll try to keep this simple. All 3 APC albums are sort of parallel to each other, like a back and forth conversation. Track by track each album is talking about the same thing but from different points of view. Compare by track number, for example, track 1 on Mer De Noms is talking to track 1 on 13th Step and track 1 on eMOTIVe, and so on through the tracks. All 3 albums has 12 songs. This part of the story basically branches off from Lateralus, "Spiral Out!!", get it? Then the story comes back together in 10,000 Days.
So if for some reason you didn't already know, "Mer De Noms" means Sea of names, so think of it as the descending path, and obviously 13th Step implies the ascending path, now think of the song The Grudge when he says "Saturn lifts you up like a child, or drags you down like a stone" and "choose 1 or 10" well refer back to lateralus for all that. Where does eMOTIVEe fit into that? Well checkout the "Extra" section where I will write a re-examined explanation of the over all story.
And then of course there's the Anima concept that I kind of explained in aenima. Also on a timeline, think of Mer De Noms as going backwards from Lateralus, and 13th Step as going forward after Lateralus, cause thats how the story is, but also coincidentally thats how they were released in real time.