  The main goal of this paper is to construct an analogue of Voevodsky's slice
filtration in the motivic unstable homotopy category. The construction is done
via birational invariants, this is motivated by the existence of an equivalence
of categories between the orthogonal components for Voevodsky's slice
filtration and the birational motivic stable homotopy categories constructed in
\cite{Pelaez:2011fk}. Another advantage of this approach is that the slices
appear naturally as homotopy fibres (and not as in the stable setting, where
they are defined as homotopy cofibres) which behave much better in the unstable
setting.
