Classical drawings of branched coverings

For a branched covering φ:M3→(S3,k), we give a description of how to embed φ−1(B) in M3 to determine the link type of φ−1(k)⊂M3, where B⊂S3 is a 3-ball in a bridge representation of k. We also relate, in the case M3≅S3, the bridge number of k with the bridge number of φ−1(k).