Interest in economic mobility stems largely from its perceived role as an equalizer of opportunities, though not necessarily of outcomes. In this paper we show that this view leads very naturally to a methodology for the measurement of social mobility which has strong parallels with the theory of progressive taxation. We characterize opportunity-equalizing mobility processes, and provide simple criteria to determine when one process is more equalizing than another. We then explain how this mobility ordering relates to social welfare analysis, and how it differs from existing ones. We also extend standard indices of tax progressivity to mobility processes, and illustrate our general methodology on intra- and intergenerational mobility data from the United States and Italy.