shalgo: To amplify on the mutual blunders at moves 42/43: the point is that after 42...a5 43.Rg4+ the d6-square is available to White's queen. (That is why 42...Qe6 was necessary.)
After 43.Rg4+ Kf8 44.Qd6#.
Therefore Black has to play 43...Kh8. Here 44.Qd6 still works, because Black can't take the rook: 44...Qxg4 45.Qxf6+ Kg8 46.Qxd8+
If 44...Qxd7 45.Qxf6#
If 44...Rxd7 45.Qf8#
Therefore, Black has to try 44...Qe6.
According to Stockfish, White can then threaten mate on the h-file to tie up the Black pieces: 45.Qf4 Qe7 46.Qh6 Rg8 47.Rh4 Rg7. After that, White can shift his pieces over to force the win of a queen for the rook: 48.Rd4 Qd8 49.Qe3 Rg8 50.Qe4 Kg7 51.Qd5 Kf8 52.Rc4 (threatening Rc8).
This long line wouldn't be easy to see at the board.