We study BAR-motion by defining a birational antichain *toggle group* generated by involutions called *toggles*. This lifts Striker's toggle group on the set of antichains of a poset to the birational realm. We construct an explicit isomorphism between this group and Einstein and Propp's group of birational order toggles, lifting an analogous one between the toggle groups of order ideals and antichains at the combinatorial level.

For certain nice families of posets, the order of BOR-motion is known to be finite, and can often be easily computed. We lift Stanley's transfer map between **C**(*P*) and **OP**(*P*) to a birational transfer map, which allows us to easily deduce certain properties of one kind of birational rowmotion from the other. We take advantage of this to derive the periodicity and order of BAR-motion on certain root and minuscule posets. We also lift a refined homomesy result of Propp and the second author from the combinatorial setting to the birational one, using an analogue of the "Stanley-Thomas" word, which cyclically rotates equivariantly with BAR-motion.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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