  We present an analysis of the quasi-stationary (QS) state of the contact
process (CP) on annealed scale-free networks using a mapping of the CP dynamics
in a one-step processes and analyzing numerically and analytically the
corresponding master equation. The relevant QS quantities determined via the
master equation exhibit an excellent agreement with direct QS stochastic
simulations of the CP. The high accuracy of the resulting data allows to probe
the strong corrections to scaling present in both the critical and
supercritical regions, corrections that mask the correct finite size scaling
obtained analytically by applying an exact heterogeneous mean-field approach.
{Our results represent a promising starting point for a deeper understanding of
the contact process and absorbing phase transitions on real (quenched) complex
networks
