Lemma 71.18.7. Let S be a scheme. Let B be an algebraic space over S. Let Z \subset B be a closed subspace. Let b : B' \to B be the blowing up with center Z. Let Z' \subset B' be a closed subspace. Let B'' \to B' be the blowing up with center Z'. Let Y \subset B be a closed subscheme such that |Y| = |Z| \cup |b|(|Z'|) and the composition B'' \to B is isomorphic to the blowing up of B in Y. In this situation, given any scheme X over B and \mathcal{F} \in \mathit{QCoh}(\mathcal{O}_ X) we have
the strict transform of \mathcal{F} with respect to the blowing up of B in Y is equal to the strict transform with respect to the blowup B'' \to B' in Z' of the strict transform of \mathcal{F} with respect to the blowup B' \to B of B in Z, and
the strict transform of X with respect to the blowing up of B in Y is equal to the strict transform with respect to the blowup B'' \to B' in Z' of the strict transform of X with respect to the blowup B' \to B of B in Z.
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