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It is introduced an analogue of the orbit-breaking subalgebra for the case offree flows on locally compact metric spaces, which has a natural approximatestructure in terms of a fixed point and any nested sequence of central slicesaround this point. It is shown that in the case of minimal flows admitting acompact Cantor central slice, the resulting $C^*$-algebra is the stabilizationof the Putnam orbit-breaking subalgebra associated to the induced homeomorphismon the central slice.

Local trivializations of suspended minimal Cantor systems and the stable orbit-breaking subalgebra