In this work, we study the impact of mobility and handover on the coverage probability of users in a multi-tier heterogeneous cellular network. Existing works have studied the coverage probability of mobile users without accounting for the impact of the handover events. As handovers can significantly impact the performance of high mobility users, in this work, we have accounted for intra-tier and inter-tier handovers while deriving the average coverage probability of a user in a multitier cellular network. Our mathematical model accurately follows the simulated network scenario. Through a detailed performance analysis for various user velocities, base station densities, and bias factors, our proposed model captures the intuition that a biased association towards higher power base station offers a higher coverage probability in high mobility scenarios.