  We study the following quantitative phenomenon in symplectic topology: In
many situations, if a Lagrangian cobordism is sufficiently small (in a sense
specified below) then its topology is to a large extend determined by its
boundary. This principle allows us to derive several homological uniqueness
results for small Lagrangian cobordisms. In particular, under the smallness
assumption, we prove homological uniqueness of the class of Lagrangian
cobordisms which, by Biran-Cornea's Lagrangian cobordism theory, induces
operations on a version of the derived Fukaya category. We also establish a
link between our results and Vassilyev's theory of Lagrange characteristic
classes. Most currently known constructions of Lagrangian cobordisms yield
small Lagrangian cobordisms in many examples.
