How does Black escape perpetual check here? In this position, what is a clear line in which Black escapes from perpetual check?

[FEN "2k5/7p/p1Q3p1/3pP3/1r2qP2/1P4PK/P7/8 b - - 0 1"]
It seems that the black king can escape via a5/

[FEN "2k5/7p/p1Q3p1/3pP3/1r2qP2/1P4PK/P7/8 b - - 0 1"]

1...Kb8 2.Qd6+ Kb7 3.Qd7+ Kb6 4.Qd8+ Kb5 5.Qb8+ Ka5 {Kc5? 6. Qd6 Kd4?? 7.Qxb4} 6.Qc7+ Rb6 7.Qc5+ Rb5 8.Qc7+ Kb4 {and you go for the hills.}


edit: 5.a4+!, noticed by @jknappen, is problematic. The right solution is rather to bring the king to a7 before covering checks with ...Rb7, as in @InertialIgnorance 's answer which should become the accepted one.