  We introduce the notion of groupoid pre-equivalences and prove that they give
rise to groupoid equivalences by taking certain quotients. Then, given an
equivalence of Fell bundles $\mathscr{B}$ and $\mathscr{C}$ and another
equivalence between $\mathscr{C}$ and $\mathscr{D}$, we construct an
equivalence between $\mathscr{B}$ and $\mathscr{D}$ out of the tensor product
bundle. As a consequence, we obtain that Fell bundle equivalence is indeed an
equivalence relation.
