We demonstrate a fully functional implementation of (per-user) checkpoint, restore, and live migration capabilities for JupyterHub platforms. Checkpointing -- the ability to freeze and suspend to disk the running state (contents of memory, registers, open files, etc.) of a set of processes -- enables the system to snapshot a user's Jupyter session to permanent storage. The restore functionality brings a checkpointed session back to a running state, to continue where it left off at a later time and potentially on a different machine. Finally, live migration enables moving running Jupyter notebook servers between different machines, transparent to the analysis code and w/o disconnecting the user. Our implementation of these capabilities works at the system level, with few limitations, and typical checkpoint/restore times of O(10s) with a pathway to O(1s) live migrations. It opens a myriad of interesting use cases, especially for cloud-based deployments: from checkpointing idle sessions w/o interruption of the user's work (achieving cost reductions of 4x or more), execution on spot instances w. transparent migration on eviction (with additional cost reductions up to 3x), to automated migration of workloads to ideally suited instances (e.g. moving an analysis to a machine with more or less RAM or cores based on observed resource utilization). The capabilities we demonstrate can make science platforms fully elastic while retaining excellent user experience.