This is a mistake which gives White's rook counter-play on the soon-to-be-opened f-file. Better was 30. ... Rb4 forcing White's rook to defend pawns.
31. fxe4 Rc4xe4 32. Ra1f1
The game is now wide open, with rooks threatening to go marauding through the pawn lines. Black must try to hang onto the d-passer.
32... b6
Immobilizing White's queen side.
33. Rf1f7 Re4e7 34. Rf7f5 Kd6c5
Preventing the White king from seizing d4.
35. Rf5f4 Re7e4
Setting a trap, which White does not fall into.
36. Rf4f7
If 36. RxRe4, PxRe4+; 37. KxPe4, Kb4 there follows a race which White looses: once the White king reaches f7, Black interposes ... g7-g6!! which costs White the game: his king will take h7, then take g6, the Black a-pawn queens first and covers the queening square of White's h-pawn.
36... Re4xg4 37. Rf7xa7 Rg4h4 38. Ra7xg7 Rh4h3
A critical in-between check which forces White's king to a less favorable square and gains a tempo for Black.
39. Kd3c2 Rh3xh2 40. Kc2c3 Rh2h3 41. Kc3c2 h5
The mad dash of the h-pawn is a diversion. It will never promote; its purpose is rather to force the White rook to chase it rather than do anything else. The trump card in Black's game is the passed d-pawn, which Black must keep in peto.
42. Rg7g6
White prepares to snap up the Black b6 pawn and advance his own b5 pawn. It is going to be a tight race.
42... h4 43. Rg6c6
43. b4+ Kxb4; Rxb6 Kxa4; Rb8 & b6 etc. was worth considering, as was 43. a5 Kxb5; axb.