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Vitrimers with bond exchange reactions (BERs) are a class of covalent adaptable network (CAN) polymers at the forefront of recent polymer research. They exhibit malleable and self-healable behaviors and combine the advantages of easy processability of thermoplastics and excellent mechanical properties of thermosets. For thermally sensitive vitrimers, a molecular topology melting/frozen transition is triggered when the BERs are activated to rearrange the network architecture. Notable volume expansion and stress relaxation are accompanied, which can be used to identify the BER activation temperature and rate as well as to determine the malleability and interfacial welding kinetics of vitrimers. Existing works on vitrimers reveal the rate-dependent behaviors of the nonequilibrium network during the topology transition. However, it remains unclear what the quantitative relationship with heating rate is, and how it will affect the macroscopic stress relaxation. In this paper, we study the responses of an epoxy-based vitrimer subjected to a change in temperature and mechanical loading during the topology transition. Using thermal expansion tests, the thermal strain evolution is shown to depend on the temperature-changing rate, which reveals the nonequilibrium states with rate-dependent structural relaxation. The influences of structural relaxation on the stress relaxation behaviors are examined in both uniaxial tension and compression modes. Assisted by a theoretical model, the study reveals how to tune the material and thermal-temporal conditions to promote the contribution of BERs during the reprocessing of vitrimers.