In order to analyze the flow stability of compressors rapidly in the design stage, a fast analysis method is developed in this paper. This method takes the base flow on each streamline at different spanwise locations as the research object and characterizes the effect of blade rows on the internal flow by establishing a body force model. Therefore, it is capable of taking the complex three-dimensional blade geometry and the abundant flow details into account, and what's more, it has a significantly high computational efficiency, which makes it available to engineering practice. Based on the eigenvalue theory, the flow stability problem is transformed into the eigenvalue problem, and the system stability is determined by the eigenvalue obtained by utilizing the singular value decomposition method. The flow stability of NASA Rotor 37 is analyzed to validate the reliability of the developed approach, and the results show that this analysis method is able to capture the process of stability deterioration with throttling and identify the blade tip region as the most unstable area. In order to further study the influence of blade geometry on compressor stability, a number of swept rotors are designed by modifying the stacking line of NASA Rotor 37. The assessment results via the developed method indicate that the forward sweep defined in this work can significantly improve the stability of the flow field in the tip region, while the backward sweep has the opposite effect.