In Wireless Sensor Networks (WSNs) the nodes can be either static or mobile depending on the requirements of each application. During the design of Medium Access Control (MAC) protocols, mobility may pose many communication challenges. These difficulties require first a link establishment between mobile and static nodes, and then an energy efficient and low delay burst handling mechanism. In this study, we investigate preamble-sampling solutions that allow asynchronous operation. We first introduce anycast transmission to ContikiMAC where a mobile node emits an anycast data packet whose first acknowledging node will serve as responsible to forward it towards the sink. Once this link is established, burst transmission can start, according to the respective burst handling mechanism of ContikiMAC. Although it is considered as negligible in the literature, such an anycast-based on-the-fly operation Georgios Z. Papadopoulos actually results in high packet duplication at the sink. Hence, we demonstrate that even a basic anycast-based MContikiMAC would fail to handle bursty traffic from mobile nodes mainly due to increased unnecessary traffic and channel occupancy. We then propose Mobility-Enhanced ContikiMAC (ME-ContikiMAC), a protocol that reduces packet duplications in the network by more than 90 % comparing to M-ContikiMAC. Moreover, our results in a 48-node scenario show that ME-ContikiMAC outperforms a number of state-of-the-art solutions (including MoX-MAC and MOBINET), by terms of reducing both delay and energy consumption.