Theorem 37.4 (Naturality):

Given a map of pairs $f:(X, A)\longrightarrow (Y, B)$ the following diagram commutes

$\begin{CD} @> >> H_n(A) @> {i} >> H_n(X) @> p >> H_n(X, A) @> \delta_n>> H_{n... ... >> H_n(B) @> i >> H_n(Y) @> {p}>> H_n(Y, B) @> >> H_{n-1}(B)@> >> \\ \end{CD}$(37.5)