  The purpose of this paper is to show how the diagrammatic expansion in
fermion exchanges of scalar products of $N$-composite-boson (``coboson'')
states can be obtained in a practical way. The hard algebra on which this
expansion is based, will be given in an independent publication.
  Due to the composite nature of the particles, the scalar products of
$N$-coboson states do not reduce to a set of Kronecker symbols, as for
elementary bosons, but contain subtle exchange terms between two or more
cobosons. These terms originate from Pauli exclusion between the fermionic
components of the particles. While our many-body theory for composite bosons
leads to write these scalar products as complicated sums of products of ``Pauli
scatterings'' between \emph{two} cobosons, they in fact correspond to fermion
exchanges between any number P of quantum particles, with $2 \leq P\leq N$.
These $P$-body exchanges are nicely represented by the so-called ``Shiva
diagrams'', which are topologically different from Feynman diagrams, due to the
intrinsic many-body nature of Pauli exclusion from which they originate. These
Shiva diagrams in fact constitute the novel part of our composite-exciton
many-body theory which was up to now missing to get its full diagrammatic
representation. Using them, we can now ``see'' through diagrams the physics of
any quantity in which enters $N$ interacting excitons -- or more generally $N$
composite bosons --, with fermion exchanges included in an \emph{exact} -- and
transparent -- way.
