For those interested: sometimes there is more than one move which will eventually win in these puzzles. However the line given in the puzzle is a result of much analysis as these are from positions in a very heavily analyzed vote chess game.
For example in the 2nd puzzle there are other ways--more slow and not as pretty--to eventually win but 4. Qb3+ is the most powerful and leads to a very nice end of the game.
4. Qb3 wins outright! 4.Qc4 allow 4...Qd5 4. Qb3 checkmates or wins a Queen or a rook..