Classical drawings of branched coverings

For a branched covering ?:M3?(S3,k), we give a description of how to embed ??1(B) in M3 to determine the link type of ??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 ??1(k).