this paper is the following theorem.

\[thm:main-theorem\] Let $ \mathbb{R}^{d} {\curvearrowright}X_{1} $ and $ \mathbb{R}^{d} {\curvearrowright}X_{2} $, $ d \ge 2 $, be free non smooth Borel flows and let $ \mathcal{D}_{i} \subseteq X_{i} $ be cocompact cross sections. For any orbit equivalence $ \phi : \mathcal{D}_{1} \to \mathcal{D}_{2} $ there are cocompressible invariant Borel subsets $ Z_{i} \subseteq X_{i} $ and a time change equivalence $ \psi : Z_{1} \to Z_{2} $ which extends $ \phi $ on $ \mathcal{D}_{1}
  \cap Z_{1}$.

A corollary of the theorem above and of the classification of hyperfinite equivalence relations [@MR1149121] is time change equivalence of Borel $ \mathbb{R}^{d} $-flows up to a compressible piece.

\[thm:time-change-equivalence-on-cocompressible\] Let $ \mathbb{R}^{d} {\curvearrowright}X_{i} $, $ i=1,2 $, $ d \ge 2 $, be free non smooth Borel flows. There are cocompressible invariant Borel sets $ Z_{i} \subseteq X $ such that the restrictions of flows onto these sets are time change equivalent.

In Section \[sec:periodic-flows\] we consider $ \mathbb{R}^{d} $-flows that are not necessarily free. The main results therein are Theorem \[thm:selection-theorem\] and Theorem \[thm:RxT-flow-tce-to-product\]. The first one shows that one can identify any $ \mathbb{R}^{d}
$-flow with a number of *free* $ \mathbb{R}^{p} \times \mathbb{T}^{q} 