  It has been suggested that the homogeneous black hole interior spacetime,
when quantized following the techniques of loop quantum cosmology, has a
resolved singularity replaced by a black-to-white hole transition. This result
has however been derived so far only using effective classical evolution
equations, and depends on details of the so-called polymerization scheme for
the Hamiltonian constraint. Here we propose to use the unimodular formulation
of general relativity to study the full quantum dynamics of this
mini-superspace model. When applied to such cosmological models, unimodular
gravity has the advantage of trivializing the problem of time by providing a
true Hamiltonian which follows a Schr\"odinger evolution equation. By choosing
variables adapted to this setup, we show how to write semi-classical states
agreeing with that of the Wheeler-DeWitt theory at late times, and how in loop
quantum cosmology they evolve through the would-be singularity while remaining
sharply peaked. This provides a very simple setup for the study of the full
quantum dynamics of these models, which can hopefully serve to tame
regularization ambiguities.
