agb2002: White has the bishop pair for a bishop, a knight and a pawn.Black threatens Bxg5.
The bishop on b2 x-rays Black's bishop and king. This suggests 44.Qxe3:
A) 44... dxe3 45.Bxf6+ Rg7 (45... Rxf6+ 46.Rg8#; 45... Qg7 46.Bxg7+ wins) 46.Rxh5+ Kg8 47.Bd5+ Rff7 (47... Qxd5 48.Rxg7#) 48.Rxg7+ Kf8 49.Rh8#.
B) 44... Bxg5 45.Rxg5
B.1) 45... Rd8 46.Bxh7
B.1.a) 46... Kxh7 (46... Qxh7 47.Bxd4+ wins) 47.Qe4+ Kh8 (47... Kh6 48.Qg6#) 48.Rxh5+ Kg8 (48... Kg7 49.Rh7+ wins) 49.Qg6+ Qg7 (49... Kf8 50.Qf6+ and mate next) 50.Qe6+ Qf7 (50... Kf8 51.Rf5+ Qf7 52.Qxf7#) 51.Rg5+ Kf8 52.Rf5 wins.
B.1.b) 46... Qxh7 47.Qe5+ Qg7 48.Qxg7#.
B.1.c) 46... a3 47.Bf5
B.1.c.i) 47... axb2 48.Qe5+ and mate next.
B.1.c.ii) 47... Qd5 48.Rxh5+ Kg8 (48... Kg7 49.Qe7+ Kg8 50.Be6#) 49.Bd5+ wins.
B.1.c.iii) 47... Qd6 48.Rxh5+ Kg8 (48... Kg7 49.Bxd4+ Qxd4 50.Qe7+ as above) 49.Qg3+ with a mate attack.
B.2) 45... Rh6 46.Bxd4+ Rff6 47.Bxf6+ Rxf6 48.Rxh5+ Kg7(8) 49.Qg3+ Kf8 (49... Kf7 50.Rh7+ wins) 50.Rh8+ Ke7 51.Rh7+ Rf7 52.Qg5+ Ke8 (else mate next) 53.Rh8+ Rf8 54.Bg6+ wins.
C) 44... a3 45.Bxh7
C.1) 45... dxe3 46.Bf5
C.1.a) 46... a(B)xb2 47.Rxh5+ Qh7 48.Rxh7#.
C.1.b) 46... Qe8 47.Rg8+ Rxg8 48.Bxf6+ Rg7 49.Bxg7+ Kg8 50.Be5+ Kf8 (50... Kf7 51.Bg6+ wins) 51.Bd6+ Kf7 52.Bg6+ wins.
C.2) 45... Kxh7 46.Rxh5#.
C.3) 45... axb2 46.Rxh5 looks winning (46... Qxh7 47.Rxh7+ Kxh7 48.Qe4+ Kh8 49.Qg6 wins).
C.4) 45... Bxg5 46.Rxg5 axb2 47.Qe5+ Kxh7 48.Rxh5+
C.4.a) 48... Kg6 49.Qg5+ Kf7 50.Rh7+ Ke8 (50.Ke6 Qe5#) 51.Qe5+ Kd8 52.Qb8+ Qc8 53.Qd6+ and mate next.
C.4.b) 48... Kg8 49.Rh8+ Kf7 50.Rh7+ Kg6 (50... Kg8 51.Qh8#) 51.Qh5+ Kf6 52.Qg5+ Ke6 53.Qe5#.