There's A Way To Get Instant Rematches In Marvel Vs. Capcom Fighting Collection: Arcade Classics
Briefly

The lack of a proper rematch feature for offline play hampers the experience, forcing players to repeatedly challenge each other after each match, unlike modern fighting games.
Using Quick Save and Quick Load is essential for making the rematch process smoother. Players can revert to before the match begins, reducing the back-and-forth hassle.
Read at Kotaku
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