The classical Blakers–Massey theorem

Let \(X\) be a topological space and let \(A, B \subseteq X\) be two subspaces whose interiors cover \(X\). Assume that \(A\) and \(B\) are connected and that their intersection \(C := A \cap B\) is (connected and) simply connected. If the pair \((A,C)\) is \((m-1)\)-connected and the pair \((B,C)\) is \((n-1)\)-connected, \(m,n \geq 3\), then the triple \((X;A,B)\) is \((m+n-2)\)-connected.