  The goal of the present paper is to compare, in a precise way, two notions of
operads up to homotopy which appear in the literature. Namely, we construct a
functor from the category of strict unital homotopy colored operads to the
category of infinity-operads. The former notion, that we make precise, is the
operadic generalization of the notion of A-infinity-categories and the latter
notion was defined by Moerdijk--Weiss in order to generalize the simplicial
notion of infinity-category of Joyal--Lurie. This functor extends in two
directions the simplicial nerve of Faonte--Lurie for A-infinity-categories and
the homotopy coherent nerve of Moerdijk--Weiss for differential graded operads;
it is also shown to be equivalent to a big nerve \`a la Lurie for differential
graded operads. We prove that it satisfies some homotopy properties with
respect to weak equivalences and fibrations; for instance, it is shown to be a
right Quillen functor.
