  Using high resolution hydrodynamical simulations, we explore the spin
evolution of massive dual black holes orbiting inside a circumnuclear disc,
relic of a gas-rich galaxy merger. The black holes spiral inwards from
initially eccentric co or counter-rotating coplanar orbits relative to the
disc's rotation, and accrete gas that is carrying a net angular momentum. As
the black hole mass grows, its spin changes in strength and direction due to
its gravito-magnetic coupling with the small-scale accretion disc. We find that
the black hole spins loose memory of their initial orientation, as accretion
torques suffice to align the spins with the angular momentum of their orbit on
a short timescale (<1-2 Myr). A residual off-set in the spin direction relative
to the orbital angular momentum remains, at the level of <10 degrees for the
case of a cold disc, and <30 degrees for a warmer disc. Alignment in a cooler
disc is more effective due to the higher coherence of the accretion flow near
each black hole that reflects the large-scale coherence of the disc's rotation.
If the massive black holes coalesce preserving the spin directions set after
formation of a Keplerian binary, the relic black hole resulting from their
coalescence receives a relatively small gravitational recoil. The distribution
of recoil velocities inferred from a simulated sample of massive black hole
binaries has median <70 km/s much smaller than the median resulting from an
isotropic distribution of spins.
