The SECCHI instruments aboard the recently launched STEREO spacecraft enable
for the first time the continuous tracking of coronal mass ejections (CMEs)
from the Sun to 1 AU. We analyze line-of-sight observations of the January
24-25, 2007 CMEs and fill the 20-hour gap in SECCHI coverage in January 25 by
performing a numerical simulation using a three-dimensional
magneto-hydrodynamic (MHD) code, the Space Weather Modeling Framework (SWMF).
We show how the observations reflect the interaction of the two successive CMEs
with each other and with the structured solar wind. We make detailed comparison
between the observations and synthetic images from our model, including
time-elongation maps for several position angles. Having numerical simulations
to disentangle observational from physical effects, we are able to study the
three-dimensional nature of the ejections and their evolution in the inner
heliosphere. This study reflects the start of a new era where, on one hand,
models of CME propagation and interaction can be fully tested by using
heliospheric observations and, on the other hand, observations can be better
interpreted by using global numerical models.