The opening montage is magnificent

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Take a tip: unless you've seen every film in the world, never use superlatives.

To my mind, the moody New York montage that opens Two For the Seesaw (1962) is better. Stunning, crisp Scope b/w photography - especially of Robert Mitchum on the Brooklyn Bridge.
https://www.youtube.com/watch?v=Bgssa5uRZYc

I wonder whether the opening of Manhattan was influenced by that film, but Allen's montage is mainly a series of arty postcards, unrelated to the theme of the story that follows (which is emotional maturity), and some of the images are a bit murky.