  We compute the Cech cohomology with integer coefficients of one-dimensional
tiling spaces arising from not just one, but several different substitutions,
all acting on the same set of tiles. These calculations involve the
introduction of a universal version of the Anderson-Putnam complex. We show
that, under a certain condition on the substitutions, the projective limit of
this universal Anderson-Putnam complex is isomorphic to the tiling space, and
we introduce a simplified universal Anderson-Putnam complex that can be used to
compute Cech cohomology. We then use this simplified complex to place bounds on
the rank of the first cohomology group of a one-dimensional substitution tiling
space in terms of the number of tiles.
