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The putative ubiquity of massive black holes (MBH) at the center of galaxies, and the hierarchical progress of structure formation along the cosmic history, together necessarily imply the existence of a large population of cosmic MBH binaries. Such systems are understood to be the loudest sources of gravitational waves at mHz frequencies, the regime that will be probed by the next Laser Interferometer Space Antenna (LISA). It has been proposed that the rate at which MBHs pair and then bind to form binaries is critically dependent upon the feedback exerted by the MBHs on the surrounding gaseous environment. Using the publicly available code GIZMO, we perform a suite of simulations aimed at studying the dynamics of a MBH pair embedded in a gaseous disk on 100 pc scale. By means of dedicated modules, we follow the dynamics of MBHs in the presence of different spin-dependent radiative feedback models, and compare the results to a benchmark case with no feedback at all. Our main finding is that feedback causes the secondary MBH to shrink its orbit at a reduced pace, when compared to models where feedback is absent. Moreover, such slower inspiral occurs on eccentric orbits, as feedback has the net effect of hampering the circularization process. Though idealized in many aspects, our study highlights and quantifies the importance of including spin-dependent feedback recipes in hydrodynamic simulations of MBH pairs, and ultimately in assessing the cosmological coalescence rate of such systems in view of their detection through gravitational waves.