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We report on high-resolution simulations that explore the orbital decay ofmassive black hole (MBH) pairs with masses between $10^5$ and $10^7 M_{\odot}$embedded in a circumnuclear gas disk (CND). An adiabatic equation of state isadopted, with a range of adiabatic indices, which maintains a smooth flow.Mergers between MBHs in this mass range would be detectable by the upcomingLaser Inteferometer Space Antenna (LISA). The orbital evolution is followedfrom the CND scale ($100$~pc) down to separations of $0.1$--$0.01$~pc at whicha circumbinary disk (CBD) could form. The decay is erratic and stronglydependent on the gas flow within the disk, that ultimately determines the nettorques experienced by the sinking MBH. Overall, we can identify threedifferent evolutionary stages: (i) an initially slow decay that leads to nosignificant change in the orbital angular momentum, resulting in somecircularization; (ii) a fast migration phase in which the orbital angularmomentum decreases rapidly; and (iii) a final, very slow decay phase, in whichorbital angular momentum can even increase, and a CBD can form. The fastmigration phase owes to disk-driven torques originating primarily from theco-orbital region of the secondary MBH, at a distance of 1--3 Hill radii. Wefind strong analogies with fast Type III migration for massive planets inprotoplanetary disks. The CBD forms only when the decay rate becomes smallenough to allow it enough time to carve a cavity around the primary MBH, atscales $\lesssim 1$~pc; when this happens, the MBH separation nearly stalls inour higher-resolution run. We suggest an empirically modified gap-openingcriterion that takes into account such timescale effects as well as otherdeviations from standard assumptions made in the literature. [Abriged]

The erratic path to coalescence of LISA massive black hole binaries in sub-pc resolution simulations of smooth circumnuclear gas disks