  We develop the notion of the active interval for a subsurface along a
geodesic in the Thurston metric on Teichmuller space of a surface S. That is,
for any geodesic in the Thurston metric and any subsurface R of S, we find an
interval of times where the length of the boundary of R is uniformly bounded
and the restriction of the geodesic to the subsurface R resembles a geodesic in
the Teichmuller space of R. In particular, the set of short curves in R during
the active interval represents a reparametrized quasi-geodesic in the curve
graph of R (no backtracking) and the amount of movement in the curve graph of R
outside of the active interval is uniformly bounded which justifies the name
active interval. These intervals provide an analogue of the active intervals
introduced by the third author in the setting of Teichmuller space equipped
with the Teichmuller metric.
