  The aim of this paper is to offer the first systematic exploration and
definition of equivalent causal models in the context where both models are not
made up of the same variables. The idea is that two models are equivalent when
they agree on all "essential" causal information that can be expressed using
their common variables. I do so by focussing on the two main features of causal
models, namely their structural relations and their functional relations. In
particular, I define several relations of causal ancestry and several relations
of causal sufficiency, and require that the most general of these relations are
preserved across equivalent models.
