I've been stuck in the following small detail which is part of the calculation of the $E^2$ term of the Serre Spectral Sequence.
Let $p: E\to B$ be a fibration where $B$ is a CW-complex. Denote by $E^p=p^{-1}(B^p)$ where $B^p$ is the p-skeleton of $B$. Let $\phi_{\alpha}: D^p \to B^p$ be the characteristic map of the p-cell $e^p_{\alpha}$. Let $p_{\alpha}: E_{\alpha}=\phi_{\alpha}^*(E) \to D^p$ be the pullback fibration and let $\partial E_{\alpha}=\partial \phi_{\alpha}^*(E) \to \partial D^p$ be the restriction. In his notes, Hatcher claims that by an excision argument we have an isomorphism \begin{eqnarray} \bigoplus_{\alpha} H_n(E_{\alpha},\partial E_{\alpha}) \to H_n(E^p,E^{p-1}). \end{eqnarray}
Can I have some help in seeing how the excision theorem is applied? It is probably an easy application but its not clear to me. Thanks!