An important clearance theme is exhibited in all its purity. It's White to play and force checkmate in four moves. What is the key?

1...Nf2 and 1...Rh2 allow 2.Qxf2# and 2.Qg8# respectively. But how do you continue after 1.Qa2 b4?

Once again, Nf2 and Rh2 run into Qxf2# and Qg8# respectively. But how do you continue after 2.Ba1 b3?

And now, what if Black plays 3...Rh2?

And what for 3...Nf2? How does White finish it off?