Featured by flexible deployment, unmanned aerial vehicles (UAVs) can form multi-tier networks in 3D space, enhancing the capacity, but this heterogeneity causes more unnecessary handovers (HOs), i.e., ping-pongs (PPs) and handover failures (HOFs). However, existing studies have not modeled the HO process in multi-tier UAV networks. This paper proposes an equivalent model for the HO process in $K$ -tier UAV networks, where nonlinear mapping rules are established from the altitude and transmit power to equivalent horizontal distances specific to HO events, then HO status during time-to-trigger (TTT) is analyzed via the mapping rules. Specifically, each trigger condition of the HO events is transformed into a circular boundary centered on the projection of the target UAV with the corresponding trigger radii. Considering the practical HO process, the HO trigger location is tractably modeled as a random variable of the path length from the start, and the signal-to-interference ratio during TTT and the residence time are analyzed through equivalent geometric relations. The results show that there exists an altitude ratio that causes the most frequent HO, which increases by 25% to 150% under different configurations. Trade-offs between HOF and PP exist in the altitude ratio and transmit power ratio, besides the HO parameters.