Suppose is an embedding of closed oriented manifolds whose normal bundle has the structure of a complex vector bundle. It is well known in both complex and symplectic geometry that one can then construct a manifold which is the blow-up of along . Assume that and that is injective. We construct an algebraic model of the rational homotopy type of the blow-up from an algebraic model of the embedding and the Chern classes of the normal bundle. This implies that if the space is simply connected then the rational homotopy type of depends only on the rational homotopy class of and on the Chern classes of the normal bundle.
"The rational homotopy type of a blow-up in the stable case." Geom. Topol. 12 (4) 1921 - 1993, 2008. https://doi.org/10.2140/gt.2008.12.1921