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In this paper, we study the blood flow dynamics in a three-dimensional (3D) idealized left ventricle of the human heart whose deformation is driven by muscle contraction and relaxation in coordination with the action of the mitral and aortic valves. We propose a simplified but realistic mathematical treatment of the valves function based on mixed time-varying boundary conditions (BCs) for the Navier-Stokes equations modeling the flow. These switching in time BCs, from natural to essential and viceversa, model either the open or the closed configurations of the valves. At the numerical level these BCs are enforced by means of the extended Nitsche's method [A. Tagliabue et al., MATHICSE report, 2015]. Numerical results for 3D idealized left ventricle obtained by means of Isogeometric Analysis are presented, discussed in terms of both instantaneous and phase-averaged quantities of interest and validated against those available in literature, both experimental and computational. The complex blood flow patterns are analysed to describe the characteristic fluid properties, to show the transitional nature of the flow, and to highlight its main features inside the left ventricle. The sensitivity of the intraventricular flow patterns to the mitral valve properties is also investigated.