Clustered star formation towards Berkeley 87 / ON2. I. Multi-wavelength
  census and the population overlap problem
  (ABRIDGED) Disentangling line-of-sight alignments of young stellar
populations is crucial for observational studies of star-forming complexes.
This task is particularly problematic in a Cygnus-X subregion where several
components, located at different distances, are overlapped: the Berkeley 87
young massive cluster, the poorly-known [DB2001] Cl05 embedded cluster, and the
ON2 star-forming complex, in turn composed of several HII regions. We aim at
providing a methodology for building an exhaustive census of young objects that
can consistently deal with large differences in both extinction and distance.
  OMEGA2000 near-infrared observations of the Berkeley 87 / ON2 field are
merged with archival data from Gaia, Chandra, Spitzer, and Herschel, as well as
cross-identifications from the literature. To address the incompleteness
effects and selection biases that arise from the line-of-sight overlap, we
adapt existing methods for extinction estimation and young object
classification, and we define the intrinsic reddening index, $R_\mathrm{int}$,
a new tool to separate intrinsically red sources from those whose infrared
color excess is caused by extinction. We also introduce a new method to find
young stellar objects based on $R_\mathrm{int}$. The flexibility of our
approach allows to overcome photometric biases in order to obtain homogeneous
catalogs of young sources.
  As a result, we find 571 objects whose classification is related to recent or
ongoing star formation. Together with other point sources with individual
estimates of distance or extinction, we compile a catalog of 3005 objects to be
used for further membership work. A new distance for Berkeley 87, ($1673 \pm
17$) pc, is estimated as a median of 13 spectroscopic members with accurate
Gaia EDR3 parallaxes. Our multi-wavelength census will serve as a basis for
disentangling the overlapped populations.
