In this largely expository note, we reexamine the construction of the homotopical Mayer-Vietoris sequence associated to a homotopy pullback. We show that in this situation, the Mayer-Vietoris sequence may be realized simply as the homotopy sequence of a suitable fibration. The usual approaches to constructing the Mayer-Vietoris sequence involve some auxiliary algebraic result, such as the Barratt-Whitehead lemma; the present approach avoids any such considerations. An additional beneficial feature of our approach is the attention paid to the bottom end of the Mayer-Vietoris sequence. Thus we are led to a cleaner proof of Proposition II.7.11 of [HMR]; moreover, we show that the converse of this latter result is also true. The homological Mayer-Vietoris sequence associated to a homotopy pushout may be established in a very similar manner, as we point out at the end of the paper.