In this thesis, we demonstrate how presheaves of labelled transition systems (LTS) acquire a very natural form of spatially induced independence on their actions when we allow a minimal amount of gluing on selected transitions within such systems. This gluing condition is characterized in the new model of LTS-adapted presheaf, and we also make use of the new model of asynchronous labelled transition system with equivalence (ALTSE) to characterize independence on actions. As such, our main result, the Theorem of Spatially Induced Independence, establishes functors from the categories of LTS-adapted presheaves to the categories of ALTSE-valued presheaves; it is a result that extends a proposition of Malcolm [SSTS] in the context of LTS-valued sheaves on complete Heyting algebras.