How does his 3 step plan by Petrosian works? [FEN &quot;r6k/3q2bp/1p6/2pPp1p1/2P1QpP1/5P2/1P2R2P/2B3K1 w - - 0 1&quot;]

Here Petrosian gives the following 3 step winning plan:
Stage 1: Tie down the black pieces to defense of the e pawn: 13.Bd2 Re8 14.Bc3 Qd6 15.Re1
Stage 2: Switch to the a file: 15..h6 Ra1 and then Ra7
Stage 3: Penetrate into the white squares.
Now what I don't understand is this: when he proceeds with stage 2 by bringing the rook to a file, isn't he removing one attacker of the e pawn? Now black's pieces will not be tied to the e pawn anymore. So, how is this plan any effective?
when he proceeds with stage 2 by bringing the rook to a file, isn't he
removing one attacker of the e pawn? Now black's pieces will not be
tied to the e pawn anymore. So, how is this plan any effective?

Currently black controls the a file with the rook on a8. The whole point of step 1. &quot;tie down black pieces defending e pawn&quot; is to force the a8 rook to give up the a file to defend the e pawn with Re8. Only when that is accomplished can white take over the a file with Ra1. The whole point of having a multi step is achieving the last step. The earlier steps are only necessary because without them the last step cannot be forced.