On parallelism of more than two strings in tangles

We give a criterion to decide when an n-string tangle in a handlebody consists of n parallel strands. and t be two arcs of an n-string tangle in a handlebody. We write s → t if the arc s is parallel to the boundary of the exterior of t without passing through the other strings. l show that n arcs t1, t2,…, tn in a handlebody are parallel, if and only if ti → tj, for all i and j such that i ≠ j and 1 ⩽ i, j ⩽ n.