In moving train networks, two-hop architecture is adopted to improve users experience by reducing the interaction between on-board users and base stations on the train route. In addition, edge networking have emerged as a solution for bringing services to the proximity of the users. However, deploying two-hop and edge networks do not guarantee a continuous service delivery for train users. When a large number of users transit from the train to the land, they experience service interruption due to control signalling storm and backhaul latency. In this paper, we propose a holistic edge service management system to provide mobile service continuity. The contribution of this paper is twofold. First, we develop an enhanced handover scheme that reduces control signals by handling user mobility at the edge. Second, we develop a pre-copy migration scheme that eliminates backhaul latency by relocating containerized applications to the user proximity across edge train networks. Our experimental results show that the two proposed solution can reduce the control signals and migration downtime by 50% and 36%, respectively.