Rook Down vs 2 Passers and Winning

The diagram below shows the winning position that was available to me in a training game played 21st April 2007. I am black. In the game my (black) king was on b4 and it was me to move. Falsely evaluating my position as lost, I quickly played a dillusional blunder: Kxb5. I was quickly punished with Bxd3+ of course. When inspecting a quick blundercheck on Fritz, to my astonishment Fritz announced black to be winning after ...Kc4 (diagram position). I intend to analyse this position deeply as it is almost hard to believe black is not only able to hold a draw but must win.

I will refer to white's first move from the diagram position as 1.

(A): 1.Rc7+ Kd4 (heading for e3 and attacking bishop). Now I will look at: 2a.Bxd3 and 2b.Kf2

2a.Bxd3 Kxd3 3.Rc1 (covering ...Bb4+ Kmoves ...e1=Q) 3...Bb4+ 4.Kf2 Kd2 (also good is the simple 4... e1=Q+ 5.RxQ BxR 6.KxB with a won pawn ending:

Diagram A 2b. 4... e1=Q+ 5.RxQ BxR 6.KxB:

6...Kc3 7.Ke2 g4 8.Kf2 Kc4 9.Kg3 Kxb5 10.Kxg4 Kc4 11.Kh5 b5 12.Kxh6 b4 13.g4 b3 14.g5 b2 15.g6 b1=Q 16.b7 Qc1+ 17.Kg6 Qc2+ 18.Kf6 Qh7 19.Kf7 Kd5 0-1

5.Rg1 (5.Re1 Bc5+ 6.Kf3 Kxe1 0-1) 5...Bc5+ 6.Kg3 (6.Kf3 e1=Q 7.RxQ (7.Rb2+ Kc3 0-1) 7...KxR 0-1) e1=Q+ 7.RxQ KxR 0-1.

2b.Kf2 Kxe4 3.Rc4+ (3.Rc8 Ba3 4.Re8+ Kd5 5.Rxe2 (5.Rd8+ Kc4 6.Rc8+ (6.Ke3?? e1=Q+ and 6.Ke1 Bb4+ #5) 6...Bc5+ 7.Ke1 (7.Kg3 e1=Q+ 0-1) 7...Kb3 8.Rxc5 bxc5 9.b6 Kc2 10.b7 d2+ 11.Kxe2 d1=Q+ 0-1) 5...Bc5+ (or just 5...dxe2 0-1) 6.Ke1 dxe2 0-1) 3...Kd5 4.Rc3 (4.Ra4 Bg7 5.Ra3 Kc4 6.Ra4+ Kxb5 7.Re4 Bc3 8.Rxe2 dxe2 9.Kxe2 0-1) 4...Kd4: a.5.Rc1 Bc5 6.Re1 Kc3+ 7.Kf3 g4+ 8.Kg3 d2 9.Rxe2 d1=Q 0-1, b.5.Rc8 Bc5 6.Re8 (6.d8 Ke4+ 7.Rd4+ (7.Ke1 Bb4+ 8.Kf2 e1=Q#) 7...Kxd4 0-1) 6...Kc4+ 7.Ke1 Bb4+ 8.Kf2 e1=Q+ 9.Rxe1 Bxe1 10.Kxe1 0-1, c.5.Rb3 Bc5 0-1.

That all goes to show that 1.Rc7 doesn't save white. Now I want to look at (B): 1.Bxd3.