  A system of k Neveu-Schwarz (NS) 5-branes of type II string theory with one
transverse direction compactified on a circle admits various unstable D-brane
systems, - some with geometric instability arising out of being placed at a
point of unstable equilibrium in space and some with the usual open string
tachyonic instability but no geometric instability. We discuss the effect of NS
5-branes on the descent relations among these branes and their physical
interpretation in the T-dual ALF spaces. We argue that if the tachyon potential
controlling these descent relations obeys certain conditions, then in certain
region in the parameter space labelling the background the two types of
unstable branes become identical via a second order phase transition, with the
geometric tachyon in one system getting mapped to the open string tachyon of
the other system. This would provide a geometric description of the tachyonic
instability of the usual non-BPS Dp-brane in ten dimensional flat space-time.
