  We compare the higher analytic torsion of Bismut and Lott of a fibre bundle
p: M -> B equipped with a flat vector bundle F -> M and a fibre-wise Morse
function h on M with a higher torsion T that is constructed in terms of a
families Thom-Smale complex associated to h and F, thereby extending previous
joint work with Bismut. Under additional conditions on F, the torsion T is
related to Igusa's higher Franz-Reidemeister torsion. As an application, we use
the higher analytic torsion to detect infinite families of smooth bundles p_i:
M -> B with diffeomorphic fibres that are homeomorphic but not diffeomorphic as
bundles.
