This article is concerned with the analysis of blood flow through arterial catheterization (widening of arteries by a balloon in the presence of mild stenosis), when blood is represented by MHD Newtonian fluid. A uniform magnetic field is applied perpendicular to the porous artery. A mathematical model is developed and analyzed by using appropriate mathematical techniques. Analytical expressions are obtained for axial velocity, flow rate, wall shear stress, and apparent viscosity and their variations with different flow parameters are illustrated in figures. In this confined annular region, the behavior of these flow variables has been explored. Its worth noting that, due to the introduction of an axial slip, velocity and flow rate will increase on one hand while wall shear stress and apparent viscosity will decrease on the other.The effects of stenosis and tapering are discussed. The study of the above model is very significant as it has direct applications in the treatment of cardiovascular diseases.