We study the problem of falsifying the assumptions behind a set of broadly applied causal identification strategies: namely back-door adjustment, front-door adjustment, and instrumental variable estimation. While these assumptions are untestable from observational data in general, we show that with access to data coming from multiple heterogeneous environments, there exist novel independence constraints that can be used to falsify the validity of each strategy. Most interestingly, we make no parametric assumptions, instead relying on that changes between environments happen under the principle of independent causal mechanisms. @en