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In bi-parametric linear optimization (LO), perturbation occurs in both the right-hand-side and the objective function data with different parameters. In this paper, the bi-parametric LO problem is considered and we are interested in identifying the regions where the optimal partitions are invariant. These regions are referred to as invariancy regions. It is proved that invariancy regions are separated by vertical and horizontal lines and generate a mesh-like area. It is proved that the boundaries of these regions can be identified in polynomial time. The behavior of the optimal value function on these regions is investigated too.