  For an $SU(2)\times U(1)$-invariant $S^3$ boundary the classical Dirichlet
problem of Riemannian quantum gravity is studied for positive-definite regular
solutions of the Einstein equations with a negative cosmological constant
within biaxial Bianchi-IX metrics containing bolts, i.e., within the family of
Taub-Bolt-anti-de Sitter (Taub-Bolt-AdS) metrics. Such metrics are obtained
from the two-parameter Taub-NUT-anti-de Sitter family. The condition of
regularity requires them to have only one free parameter ($L$) and constrains
$L$ to take values within a narrow range; the other parameter is determined as
a double-valued function of $L$ and hence there is a bifurcation within the
family. We found that {\it{any}} axially symmetric $S^3$-boundary can be filled
in with at least one solution coming from each of these two branches despite
the severe limit on the permissible values of $L$. The number of infilling
solutions can be one, three or five and they appear or disappear
catastrophically in pairs as the values of the two radii of $S^3$ are varied.
The solutions occur simultaneously in both branches and hence the total number
of independent infillings is two, six or ten. We further showed that when the
two radii are of the same order and large the number of solutions is two. In
the isotropic limit this holds for small radii as well. These results are to be
contrasted with the one-parameter self-dual Taub-NUT-AdS infilling solutions of
the same boundary-value problem studied previously.
