  Given two locally compact Hausdorff groupoids $G$ and $H$ and a
$(G,H)$-equivalence $Z$, one can construct the associated linking groupoid $L$.
This is reminiscent of the linking algebra for Morita equivalent
$C^*$-algebras. Indeed, Sims and Williams reestablished Renault's equivalence
theorem by realizing $C^*(L)$ as the linking algebra for $C^*(G)$ and $C^*(H)$.
Since the proof that Morita equivalence preserves exactness for $C^*$-algebras
depends on the linking algebra, the linking groupoid should serve the same
purpose for groupoid exactness and equivalence. We exhibit such a proof here.
