  We introduce the notion of locally visible and locally Gromov hyperbolic
domains in $\mathbb C^d$. We prove that a bounded domain in $\mathbb C^d$ is
locally visible and locally Gromov hyperbolic if and only if it is (globally)
visible and Gromov hyperbolic with respect to the Kobayashi distance. This
allows to detect, from local information near the boundary, those domains which
are Gromov hyperbolic and for which biholomorphisms extend continuously up to
the boundary.
