Crazy Finish

I HAD been two pawns up and winning for much of the game when the following position was reached in round four of the 'Paignton' premier.

White to make his 43rd move in Spanton (1881/168) - Daniel Rosen (2012/171)

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43.b3?
White is much better after 43.Bd5!? or 43.Bb3, in each case preventing Black's rook from occupying the back rank. The latter was probably the most practical move, but Bd5 is also good, according to analysis by the engines Stockfish10 and Komodo 10, who give 43...c6 44.b4 Qb5 45.c4 Qxb4 46.Be6 Re7 (invading with 46...Rd1? is now ineffective) 47.Bxg4 hxg4 48.Rf2! (48.Qxg4 allows serious counterplay with 48...Rf7) Qxc4 49.Qxg4.
43...Rd1 44.Re1
Also equal, according to the engines, is 44.Qf3!? Rg1+ 45.Kh3 Qe7 (only move), eg 46.Rd2 c6! (another only move) 47.Qd3 Rd1! (yet another only move) 48.Rxd1 Nf2+ 49.Kg2 Nxd3 50.Rxd3, and the position is apparently dead-equal. However, this was worth a try as it is easier for Black to go wrong.
44...Rd2+ 45.Re2?
This loses. White had to play 45.Be2, when 45...Rxa2 is another dead-equal position, according to the engines.
45...Rd1?
Black wins with 45...Ne3+ as White is losing a piece to ...Nxc4.
46.Re1 ½–½