Gypsy: <Sastre: ... How is White lost after <55.Bxb6 axb6 56.Kb5 Na7+ 57.Kxb6 Nc8+ 58.Kb7 c4 59.Kxc8 c3 60.a7 c2 61.a8=Q c1=Q+ 62.Kd8>?>That is a very good question. I think this is a theoretical win for Black, but a difficult one. Let us take things from the top of the order:
(1) The suggested <57...Nc8+?> must be an error because it loses a key tempo. After eschewing the move, we get,
55.Bxb6! axb6 56.Kb5 Na7+ 57.Kxb6 <c4> 58.Kxa7 c3 ...
(2) At his point, <59.Kb7?> would be an error, as we will see shortly, but either <59.Kb6> or <59.Kb8> look playable. I am not sure which is better.
(3) After the K move, Black finishes the foot race a tempo up.
59...c2 60.a7 c1Q 61.a1Q...
(4) We can now see why <59.Kb7?> would have been a mistake: With White K on b7, Black would now been able to force an exchange of the queens (61...Qh1+) and transform the game into an easily won pawn endgame.
With White K on either b6 or b8, however, it is not at all clear to me whether there is a sequence of checks that forces the desired Q swap.
(5) Therefore, it may be best for Black to keep White K cut off and immediately collect the h-pawn and put his trust into the Q+P vs Q endgame.
<61...Kxh6>
(6) Since (i) White K is cut off from the remaining pawn, and since (ii) this remaining pawn stands on the f-file, my endgame theory books claim that this Q ending is a forced win for Black.