Ordered-state visit times in a reversible chain

Under a stationary initial law, reversal leaves the law of a finite reversible-chain path unchanged. The first time an ordered occurrence of state $a$ then state $b$ appears therefore has the same distribution as the reverse ordered occurrence. Decomposition at the first entrance relates this symmetry to differences of mean hitting times. If positive diagonal return times are used instead of zero diagonal entrance times, their stationary-weighted terms cancel by Kac's lemma.