With the network densification, frequent handovers may degrade mobility reliability, cause heavy signaling load thus blocking the improvement of network capacity. This paper aims at reducing cost in terms of handover in dense networks, deriving compact expressions of network performance metric, including handover probabilities as well as the mobility-aware downlink data rate, under a multi-connectivity mobility model in user-centric ultra-dense networks (UUDNs). Specifically, the nearest M access points (APs) in mobile user's vicinity serve the user for data transmission, while the best one among them is for control, which reduces handover probability and network overheads without a loss in the throughput performance gain. Based on the scheme, handover probabilities are derived for arbitrary movement trajectory in the UUDN, where the locations of APs are modeled as a homogeneous Poisson point process, and then is included in handover cost to derive the downlink rate for mobile users. It is shown that the handover probability in control-plane can considerably be decreased by at least 30% compared with the traditional single connectivity network. What is more, the downlink rate can be improved significantly by 2× compared with single connectivity.