This paper describes the investigations performed to better understand unsteady flows that develop in a three-stage high-pressure compressor. More specifically, this study focuses on rotor-stator interactions and tip leakage flow effects on overall performance and aerodynamic stability. The investigation method is based on three-dimensional unsteady RANS simulations, considering the natural spatial periodicity of the compressor. Indeed, all information related to rotor-stator interactions can be computed. A comparison is first done with experimental measurements to outline the capacity of the numerical method to predict overall performance and unsteady flows. The results show that the simulation correctly estimates most flow features in the multistage compressor. Then numerical data obtained for three configurations of the same compressor are analyzed and compared. Configurations 1 and 2 consider two sets of tip clearance dimensions and a casing treatment based on a honeycomb design is applied for configuration 3. Detailed investigations of the flow at the same operating line show that the tip leakage flow is responsible for the loss of stability in the last stage. An increase by 30% of the tip clearance dimension dramatically reduces the stable operating range (by 40% with respect to the standard configuration). A modal analysis shows that the stall process in this case involves the perturbation of the flow in the last rotor by upstream stator wakes, leading to the development of a rotating instability. The control device designed and investigated in this study allows for reducing the sensitivity of the compressor to tip leakage flow by recovering the initial stable operating range.