In transport networks, a multi-ring architecture is very useful to facilitate network planning and to design and provide more resilient services for customers. Unlike traditional synchronous optical network multi-rings, the service resiliency of Ethernet-based multi-rings is significantly impacted by the ring hierarchy because a link or node failure in a certain level ring triggers filtering database flush actions in all higher level rings as well as in the ring with the failure, and consequently a large amount of duplicated data frames may be flooded. In this paper, we investigate how the ring hierarchy impacts the service resiliency of multi-ring networks. Based on extensive experiments on various single- and multiple-link failures, we suggest two effective inter-ring connection rules to minimize the transient traffic and to ensure more resilient multi-ring networks. In addition, we consider a flush optimization technique called e-ADV, and show that the combination of e-ADV and multi-ring structures satisfying our inter-ring connection rules results in a more attractive survivability performance.