Blakers-Massey theorem

This fact is related to: excisive triads

Statement

Let $(X;X_1,X_2)$ be an excisive triad, viz $X$ is a topological space and $X_1$, $X_2$ are subspaces such that the union of the interiors of $X_i$s is $X$). Then if $(X_1,X_1\cap X_2)$ is $(n-1)$-connected and $(X_2,X_1\cap X_2)$ is $(m-1)$-connected, the inclusion map ${\pi }_q(X_1,X_1\cap X_2)\to {\pi }_q(X,X\cap X_2)$ is an isomorphism for $q<m+n-2$ and a surjection for $q=m+n-2$.