Unimodular gravity can be formulated so that transverse diffeomorphisms and
Weyl transformations are symmetries of the theory. For this formulation of
unimodular gravity, we work out the two-point and three-point $h_{\mu\nu}$
contributions to the on-shell classical gravity action in the leading
approximation and for an Euclidean AdS background. We conclude that these
contributions do not agree with those obtained by using General Relativity due
to IR divergent contact terms. The subtraction of these IR divergent terms
yields the same IR finite result for both unimodular gravity and General
Relativity. Equivalence between unimodular gravity and General Relativity with
regard to the gauge/gravity duality thus emerges in a non trivial way.
