Abstract: This work investigates the classical and quantum duality between the SIM (1)-Maxwell-Chern-Simons (MCS) model and its self -dual counterpart. Initially, we focus on free -field cases to establish equivalence through two distinct approaches: comparing the equations of motion and utilizing the master Lagrangian method. In both instances, the classical correspondence between the self -dual and MCS dual fields undergoes modifications due to very special relativity (VSR). Specifically, the duality is established when the associated VSR-mass parameters are identical, and the dual field is introduced through a non -local VSR correction. Furthermore, we analyze the duality when the self -dual model is minimally coupled to fermions. As a result, we demonstrate that Thirring-like interactions, corrected for non -local VSR contributions, are included in the MCS model. Additionally, we establish the quantum equivalence of the models by performing a functional integration of the fields and comparing the resulting effective Lagrangians.