do not preserve any given measure turns out to be more important than the necessity to define equivalences on every orbit (as opposed to almost everywhere). We recall that an equivalence relation $ \cber $ on a standard Borel space $ X $ is said to be smooth if there is a Borel map $ f : X \to
\mathbb{N}^{\mathbb{N}} $ such that $$x \cber* y \iff f(x) = f(y).$$ For equivalence relations arising as orbit equivalence relations of Polish group actions this is equivalent[^3] to existence of a Borel transversal — a Borel set that intersects each equivalence class in a single point.

Miller and Rosendal posed a question whether any two free Borel $ \mathbb{R}^{d} $-flows are time change equivalent. This paper makes a contribution in this direction.

Main results {#sec:main-results}
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Many constructions in Borel dynamics and ergodic theory have to deal with two kinds of issues — “local” and “global”. Global aspects refer to properties that hold relative to many (usually all) orbits. Local aspects of a construction, on the other hand, reflect behavior that is local to any given orbit. For instance, the property of $ \phi : X \to Y $ being an orbit 