Excision Axiom of Homology

Let \((X,A)\) be a pair of spaces and \(U \subseteq A\) a subspace such that

\begin{align*} \overline{U} \subseteq \mathrm{int}(A) \end{align*}

Then the inclusion

\begin{align*} \iota: (X \setminus U, A \setminus U) \rightarrow (X,A) \end{align*}

induces an isomorphism on homology