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The 3GPP has provided its first standard specifications for network slicing in the recent Release 15. The fundamental principles are specified which constitute the standard network slicing framework. These specifications, however, lack the session continuation mechanisms among slices, which is a fundamental requirement to achieve inter-slice mobility. In this paper, we propose three solutions which enable session continuation among slices in the current 3GPP network slicing framework. These solutions are based on existing, well-established standard mechanisms. The first solution is based on the Return Routability/Binding Update (RR/BU) procedure of the popular Internet standard, Mobile IPv6 (MIPv6). The second solution is based on the 3GPP standard GPRS Tunnelling Protocol User Plane (GTPv1-U), which establishes a GTP tunnel between previous and new slice for session continuation. The third solution is a hybrid solution of both MIPv6-RR/BU and GTPv1-U protocols. We compare the performance of all these solutions through analytical modelling. Results show that the GTPv1-U based and the hybrid MIPv6/GTPv1-U solutions promise lower service disruption latency, however, incur higher resource utilization overhead compared to MIPv6-RR/BU and 3GPP standard PDU Session Establishment process.