Many fluid flow problems involve localized effects within a larger flow domain, with boundary layers close to solid boundaries being one of the most common. Accurate and realistic computational analysis of such problems requires that the local flow behavior is properly represented by a numerical formulation with affordable computational cost. Among several strategies developed in the computational mechanics to deal with multiscale phenomena, the Arlequin method proposes overlapping a local discretization to a global one and gluing both models by Lagrange multipliers field, being successful in the solid mechanics context, but unexplored for CFD analysis. In this work, we introduce the Arlequin method to the numerical analysis of unsteady incompressible flows. Differently from the previous works involving incompressible media, a stabilized finite element formulation is employed. To improve stability and conditioning of the algebraic system of equations, we propose a novel Residual-Based Stabilized Arlequin Formulation. The resulting formulation is tested in various numerical examples, considering structured and unstructured, coincident and non-coincident finite element discretization, Stokes problems and convection dominated Navier-Stokes problems, steady and transient cases, showing the methodology precision and robustness.