Levine's motivic comparison theorem revisited

For a field of characteristic zero Levine has proved in [12], Part I, Ch. VI, 2.5.5, that the triangulated tensor categories of motives defined in [16] and [121 are equivalent. Using some results of [7], in this paper we show that the strategy of Levine's proof can also be applied on every perfect field to the categories of triangulated motives with rational coefficients or to the pseudo-abelian hulls of the integral tensor subcategories generated by motives of smooth projective schemes.