  We show that under appropriate assumptions, a blown-up corona of a relatively
hyperbolic group is equivariant and the compactification of the universal space
for proper action by the blown-up corona is contractible. As a corollary, we
establish the formula to determine the covering dimension of the blown-up
corona by the cohomological dimension of the group. We also show that the
blown-up corona of a hyperbolic group with respect to an almost malnormal
family of quasiconvex subgroups is homeomorphic to the Gromov boundary of the
group.
