Carlsen's Corresponding Squares

In the following puzzle, it is Black (Levon Aronian) to play. White (Magnus Carlsen) just played pawn at g2 to g4. Black can choose some critical corresponding squares in this position. He can choose b2 for the rook. b1 and f7 are squares playable for the bishop to take or go. But Levon Aronian (currently one of the best players) choose b1 for the rook, adding White winning advantages quicker.




The following is the game in PGN format.

[Event "London Chess Classic"]
[Site "London ENG"]
[Date "2012.12.02"]
[EventDate "2012.12.01"]
[Round "2"]
[Result "1-0"]
[White "Magnus Carlsen"]
[Black "Levon Aronian"]
[ECO "C77"]
[WhiteElo "?"]
[BlackElo "?"]
[PlyCount "117"]

1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.d3 b5 6.Bb3 Bc5 7.Nc3 O-O 8.Nd5 Nxd5 9.Bxd5 Rb8  0.O-O Ne7 11.Nxe5 Nxd5 12.exd5 Re8 13.d4 Bf8 14.b3 Bb7 15.c4 d6 16.Nf3 Qf6 17.Be3 Bc8   8.Qd2 Qg6 19.Kh1 h6 20.Rac1 Be7 21.Ng1 Bg5 22.Bxg5 Qxg5 23.Rfd1 bxc4 24.bxc4 Qxd2 25.Rxd2 a5 26.h3 Rb4 27.Nf3 Bf5 28.c5 Kf8 29.Nh2 Reb8 30.Ng4 Rb1 31.Rxb1 Rxb1+ 32.Kh2 a4 33.Ne3 Bg6 34.Kg3 Rb4 35.Kf3 Ke7 36.Ke2 Kd7 37.f3 Rb5 38.Nd1 Rb4 39.c6+ Kc8 40.Nc3 f6 41.Ke3 Rc4 42.Ne2 a3 43.h4 Rb4 44.g4 Rb1 45.h5 Bh7 46.f4 f5 47.g5 Rh1 48.Ng3 Rh3 49.Kf3 hxg5 50.fxg5 g6 51.Re2 Kd8 52.hxg6 Bxg6 53.Re6 Bf7 54.g6 Bg8 55.g7 f4 56.Kxf4 Rh2 57.Nf5 Rxa2 58.Rf6 Re2 59.Rf8+ 1-0