  In the context of massive gravity theories, we study holographic flows driven
by a relevant scalar operator and interpolating between a UV 3-dimensional CFT
and a trans-IR Kasner universe. For a large class of scalar potentials, the
Cauchy horizon never forms in presence of a non-trivial scalar hair, although,
in absence of it, the black hole solution has an inner horizon due to the
finite graviton mass. We show that the instability of the Cauchy horizon
triggered by the scalar field is associated to a rapid collapse of the
Einstein-Rosen bridge. The corresponding flows run smoothly through the event
horizon and at late times end in a spacelike singularity at which the
asymptotic geometry takes a general Kasner form dominated by the scalar hair
kinetic term. Interestingly, we discover deviations from the simple Kasner
universe whenever the potential terms become larger than the kinetic one.
Finally, we study the effects of the scalar deformation and the graviton mass
on the Kasner singularity exponents and show the relationship between the
Kasner exponents and the entanglement and butterfly velocities probing the
black hole dynamics. Differently from the holographic superconductor case, we
can prove explicitly that Josephson oscillations in the interior of the BH are
absent.
