= Solution
The commutative diagram of short exact sequences of complexes induces a commutative diagram between the two long exact homology sequences from part (b). If any two vertical chain maps induce isomorphisms in every degree, then in each five-term window four of the five vertical homology maps are isomorphisms. The <Five lemma> makes the remaining map an isomorphism. Rotating the window handles each of the three possible missing columns, proving the two-out-of-three assertion.
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