In this paper we will investigate dynamic stability of percolation for the stochastic Ising model and the contact process. We also introduce the notion of downward and upward ɛ-movability which will be a key tool for our analysis.
Erik I. Broman. Jeffrey E. Steif. "Dynamical stability of percolation for some interacting particle systems and ɛ-movability." Ann. Probab. 34 (2) 539 - 576, March 2006. https://doi.org/10.1214/009117905000000602