  We study the inspiral of double black holes orbiting inside a massive
rotationally supported gaseous disk, with masses in the Laser Interferometer
Space Antenna (LISA) window of detectability. Using high-resolution SPH
simulations, we follow the black hole dynamics in the early phase when
gas-dynamical friction acts on the black holes individually, and continue our
simulation until the form a close binary. We find that in the early sinking the
black holes loose memory of their initial orbital eccentricity if they
co-rotate with the gaseous disk. As a consequence the massive black holes form
a binary with very low eccentricity. During the inspiral, gravitational capture
of gas by the black holes occurs mainly when they move on circular orbits and
may ignite AGN activity: eccentric orbits imply instead high relative
velocities and weak gravitational focusing.
