In this paper, we present an architecture for transparent service continuity for cloud-enabled WiFi networks called ARNAB: ARchitecture for traNsparent service continuity viA douBle-tier migration. The term arnab means rabbit in Arabic. It is dubbed for the proposed service architecture because a mobile-user service with ARNAB behaves like a rabbit hopping through the WiFi infrastructure. To deliver continuous services, deploying edge clouds is not sufficient. Users may travel far from the initial serving edge and also perform multiple WiFi handoffs during mobility. To solve this, ARNAB employs a double-tier migration scheme. One migration tier is for user connectivity, and the other one is for edge applications. Our experimental results show that ARNAB can not only enable continuous service delivery but also outperform the existing work in the area of container live migration across edge clouds.