We investigate the coevolution of massive black holes (MBHs) and host in galaxy mergers. MBHs are found in the centers of most nearby galaxies, and galaxy mergers occur throughout the Universe. It is often assumed that they trigger QSO/AGN activity. However, this is a simplification, as this conclusion was mostly drawn from relatively low-resolution simulations of 1:1 mergers. We ask instead which galaxy mergers do trigger MBH accretion, and when activity is triggered during a merger. To this end, we focus on the most cosmologically relevant galaxy mergers: unequal mass mergers over a wide range of orbital configurations. Using high resolution N-body SPH simulations, we track star formation, MBH accretion, and associated feedback as the MBHs move from separations of tens of kiloparsecs to tens of parsecs. We focus on the role of merger triggered gaseous inflows in driving both central starbursts and efficient MBH accretion. We use these simulations also to study the dynamical evolution of MBHs, with the aim of learning when galaxy mergers may lead to MBH-MBH mergers and eventually estimate the relative contribution of accretion and mergers in growing the MBH population.