Edge clouds are emerging as a popular paradigm of computation. In edge clouds, computation and storage can be distributed across a large number of locations, allowing applications to be hosted at the edge of the network close to the end-users. Virtual machine live migration is a key mechanism which enables applications to be nimble and nomadic as they respond to changing user locations and workload. However, VM live migration in edge clouds poses a number of challenges. Migrating VMs between geographically separate locations over slow wide-area network links results in large migration times and high unavailability of the application. This is due to network reconfiguration delays as user traffic is redirected to the newly migrated location. In this paper, we propose the use of multi-path TCP to both improve VM migration time and network transparency of applications. We evaluate our approach in a commercial public cloud environment and an emulated lab based edge cloud testbed using a variety of network conditions and show that our approach can reduce migration times by up to 2X while virtually eliminating downtimes for most applications.