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In this talk, I will present the continuous dependence on the initial data for the solutions of 3-D incompressible anisotropic Navier-Stokes equations in the anisotropic type functional spaces. I will also show the non-uniform continuity of the data-to-solution map in the same functional spaces which makes sharp contrast with the corresponding result for the classical 3-D Navier-Stokes equations. This is joint work with Professor Ping Zhang.