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Jeff Strom
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I suggest you look at Mather's "Hurewicz Theorems for Pairs and Squares" in which Blakers-Massey is derived from his Cube Theorems.

The basic inputs to the cube theorems are: (1) Hurewicz/Dold local-to-global criteria for fibrations (or weak fibrations) and (2) the pullback of a cofibration by a fibration is a cofibration.

Jeff Strom
  • 12.5k
  • 3
  • 48
  • 76