Pulmonary vessel segmentation is the key application of AI in lung disease diagnosis and surgical planning. Compared with manual labeling, automatic labeling of pulmonary vessels using an AI-based medical image segmentation method has the advantages of low cost, high accuracy, and efficiency, which is the development trend of medical images. In terms of pulmonary vessel segmentation, FCN and U-Net are the most widely used pulmonary vessel segmentation methods based on deep learning. However, the precision of pulmonary vessel segmentation, especially the small vessels, tends to be poor by such methods. Therefore, to solve the above problem, Multi-Scale Interactive U-Net (MSI-U-Net) is proposed. In MSI-U-Net, three decoder branches are used to extract small-scale, middle-scale and large-scale vessels respectively, which can improve the accuracy of small vessel segmentation by enhancing the representational ability of small vessels. In addition, to solve the problem of small vessel information loss caused by down-sampling, we introduce the attention mechanism into the skip-layer connection and propose a cross-layer aggregation module (CLA). Among the three decoder branches, a multi-scale information interaction strategy (MSIIS) is proposed based on transfer learning, which can effectively enhance the correlation of multi-scale vessels in lung CT images. In the training stage, we propose a scale-induced supervision strategy (SISS). This strategy uses the idea of fusion first and then supervision, which effectively solves the problem of inconsistency in multi-scale vessels classification, thereby reducing the segmentation errors. Finally, we use feature transmission instead of convolution parameter sharing to realize the multi-scale information interaction strategy, and propose an extension scheme called Multi-Level Cascade Interactive U-Net (MLCI-U-Net). The experimental results indicate that our MSI-U-Net and MLCI-U-Net have better performance than other state-of-the-art methods on pulmonary vessel segmentation. Specifically, the best Dice similarity coefficient (DSC), Sensitivity and Precision are obtained by the proposed methods to segment pulmonary vessels.