Missiles-in-Control Chess Puzzle: How does White Win?

How good are you at controlling the diagonals on the chess board? Let’s take a look at this position from the game Burzlaff – Stark, Oschatz, 1958. White has huge center control, but the Queen is under attack. White is also troubled about the Rook on d5. So, what would you do if you were playing White?

Burzlaff – Stark

Result: 1-0
Site: Oschatz
Date: 1958
[…] 1.♕xh6+ gxh6

1…♗h7 2.e6 threatening checkmate with Qg7 2…♖f6
2…♗xf2+ 3.♔h1 ♗d4 (3…♕c7 4.♖h5 (4.♗e4)) 4.♗xd4 ♖f6 5.♗xf6 gxf6 6.e7 (6.♖xa5)

(2…♖g8 3.♗e4) 3.♗xf6 ♕c7 (3…♗xf2+ 4.♔h1 gxf6 5.♕xf6+ ♔g8 6.♖xd8+ ♕xd8 7.♕xd8+) 4.♖xd8+ ♕xd8 5.♕xg7#

2.e6+ ♔h7 (2…♕c3 3.♗xc3+ ♗d4 4.♗xd4+ ♖f6 5.♗xf6+ ♔h7 6.♗e4#) 3.♗e4+ ♖f5 4.♗xf5#

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