  The transient number of a knot K, denoted tr(K), is the minimal number of
simple arcs that have to be attached to K, in order that K can be homotoped to
a trivial knot in a regular neighborhood of the union of K and the arcs. We
give a lower bound for tr(K) in terms of the rank of the first homology group
of the double branched cover of K. In particular, if t(K)=1, then the first
homology group of the double branched cover of K is cyclic. Using this, we can
calculate the transient number of many knots in the tables and show that there
are knots with arbitrarily large transient number.
