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It is shown that transient graphs for the simple random walk do not admit a nearest neighbor transient Markov chain (not necessarily a reversible one), that crosses all edges with positive probability, while there is such chain for the square grid Z^2. In particular, the d-dimensional grid Z^d admits such a Markov chain only when d=2. For d=2 we present a relevant example due to Gady Kozma, while the general statement for transient graphs is obtained by proving that for every transientarXiv:1711.03479v4 fatcat:ong6of5xajbmxb7bokxmaawr2m