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Since this question is about homotopical excision, I refer to my recent answer to

What is the intuition behind the Freudenthal suspension theorem?

Since this question is about homotopical excision, I refer to my recent answer to

What is the intuition behind the Freudenthal suspension theorem?

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Ronnie Brown
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Since this question is about homotopical excision, I refer to my recent answer to

What is the intuition behind the Freudenthal suspension theorem?