Classical drawings of branched coverings

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