  Topological ordered phases are related to changes in the properties of their
quasi-particle excitations (anyons). We study these relations in the framework
of projected entanglement pair states (\textsf{PEPS}) and show how condensing
and confining anyons reduces a local gauge symmetry to a global on-site
symmetry. We also study the action of this global symmetry over the
quasiparticle excitations. As a byproduct, we observe that this symmetry
reduction effect can be applied to one-dimensional systems as well, and brings
about appealing physical interpretations on the classification of phases with
symmetries using matrix product states (\textsf{MPS}). The case of
$\mathbb{Z}_2$ on-site symmetry is studied in detail.
