  We present the first comprehensive analysis of the unitarity thresholds and
anomalous thresholds of scattering amplitudes at two loops and beyond based on
the loop-tree duality, and show how non-causal unphysical thresholds are
locally cancelled in an efficient way when the forest of all the dual on-shell
cuts is considered as one. We also prove that soft and collinear singularities
at two loops and beyond are restricted to a compact region of the loop
three-momenta, which is a necessary condition for implementing a local
cancellation of loop infrared singularities with the ones appearing in real
emission; without relying on a subtraction formalism.
