Transition of additive and non-additive pulsatile flows through a simple 3D model of arterial stenosis is investigated by using a large eddy simulation (LES) technique. We find in both the pulsatile cases that the interaction of the two shear layers, one of which separates from the nose of the stenosis and the another one from its opposite wall, causes recirculation in the flow downstream of the stenosis where the nature of the transient flow becomes turbulent. The strength of this recirculation is found to be quite high from the non-additive pulsations when the flow Reynolds numbers, Re>or=1500, for which both the pressure and shearing stresses take on an oscillating form at the post-stenotic region. Potential medical consequences of these results are discussed in the paper. In addition, some comparisons of the non-additive pulsatile results are given with those of both the additive pulsatile and steady flows. The capability of using LES to simulate the pulsatile transitional flow is also assessed, and the present results show that the smaller (subgrid) scales (SGS) contributes about 78% energy dissipation to the flow when the Reynolds number is taken as 2000. The level of SGS dissipation decreases as the Reynolds number is decreased. The numerical results are validated with the experimental data available in literature where a quite good agreement is found.