This paper points out an important threat that application-level Garbage Collection (GC) creates to the use of non-volatile memory (NVM). Data movements incurred by GC may invalidate the pointers to objects on NVM, and hence harm the reusability of persistent data across executions. The paper proposes the concept of movement-oblivious addressing (MOA), and develops and compares three novel solutions to materialize the concept for solving the addressability problem. It evaluates the designs on five benchmarks and a real-world application. The results demonstrate the promise of the proposed solutions, especially hardware-supported Multi-Level GPointer, in addressing the problem in a space- and time- efficient manner.