We discussed some accelerating anisotropic dark energy models with dynamic pressure anisotropies along different spatial directions in the framework of General Relativity. A spatially homogeneous but anisotropic LRSBI space time is considered to model the universe. Explicit expressions for directional pressure anisotropies are obtained in terms of the deceleration parameter. This provides us an opportunity to tune the evolutionary aspect of the pressure anisotropies through the evolving nature of the deceleration parameter. It is found that, for models predicting constant deceleration parameter, the pressure anisotropies are maintained throughout the cosmic evolution. However, for models simulating a signature flipping deceleration parameter, the pressure anisotropies along the sym- metry axis and symmetry plane are found to evolve dynamically and continue along with the cosmic expansion.