  The formation of massive black hole binaries (MBHBs) is an unavoidable
outcome of galaxy evolution via successive mergers. However, the mechanism that
drives their orbital evolution from parsec separations down to the
gravitational wave (GW) dominated regime is poorly understood, and their final
fate is still unclear. If such binaries are embedded in gas-rich and turbulent
environments, as observed in remnants of galaxy mergers, the interaction with
gas clumps (such as molecular clouds) may efficiently drive their orbital
evolution. Using numerical simulations, we test this hypothesis by studying the
dynamical evolution of an equal-mass, circular MBHB accreting infalling
molecular clouds. We investigate different orbital configurations, modelling a
total of 13 systems to explore different possible impact parameters and
relative inclinations of the cloud-binary encounter. We focus our study on the
prompt, transient phase during the first few orbits when the dynamical
evolution of the binary is fastest, finding that this evolution is dominated by
the exchange of angular momentum through gas capture by the individual black
holes and accretion. Building on these results, we construct a simple model for
evolving a MBHB interacting with a sequence of clouds, which are randomly drawn
from reasonable populations with different levels of anisotropy in their
angular momenta distributions. We show that the binary efficiently evolves down
to the GW emission regime within a few hundred million years, overcoming the
'final parsec' problem regardless of the stellar distribution.
