meppi: 29. Rxg2+ although a speculative move, does complicate the game, and gives white chances to go wrong.
As whiteshark has shown earlier 31. e6+ is a very strong move which starts a big attack down the open e-file. But it was difficult to see what to do after Re1+ so I turned on to Fritz 6 which gave me this attack.
"31. e6+ Kxe6
32. Re1+ Kd7
33. Re7+ Kxe7
34. Qc7+ Kf6 (Kf8 - 35. Bb4 or Ke6 35. Re1+)
35. Bxd4+ " Fritz 6.
A hard attack to see especially the sacrifice 33. Re7+
31. e6 was indeed the winning move for white in this game.
38. Rg1+ is a good move, trading the exchange for the dangerous bishop pair, white also had thoughts of a strong attack involving Qxh7 and using both bishops if black tried to hold onto the exchange.
For whiterook48. 41. Qg7+ is not an entirely bad move, it trades queens of the board and defends the b pawn. However, after the Q's are gone it is a knight vs bishop endgame where white will be playing for the win and black for the draw.
Maybe a better move would have been 41. Ke6 or Kf6 allowing 42. Qxb7 and then counterattacking with 42. Qe3+
43. Kh1 Nxf3
In fact this attack is so strong that white may not even take the b pawn (which excludes the queen from defense of the king). 41. Qg7+ is bad because it ends pretty much any of blacks hopes of winning unless white seriously blunders.
55. Ne5 is annotated as "a good move" because it wins back the pawn after 56. Bxb7 Nd3
57. b3 Nb4+
58. K any Nxa2
Where all black needs to do is defend the a pawn with his king and knight, or kamikaze capture the b pawn with the knight to draw the game.
In the endgame Black made a strategic error by playing 61. Kd8
Better would have been moving the King to c5 where it would blockade the position with the knight and secure a draw.
This would have been done like so:
62. Kb7 Kd6
63. Kxa7 Kc5
The position in this variation is the same as the one that occurred in the game except the king is on c5 instead of c7.
both may be draws but it seems easier to draw with the black K on c5.