  Coupling dynamics of the states of the nodes of a network to the dynamics of
the network topology leads to generic absorbing and fragmentation transitions.
The coevolving voter model is a typical system that exhibits such transitions
at some critical rewiring. We study the robustness of these transitions under
two distinct ways of introducing noise. Noise affecting all the nodes destroys
the absorbing-fragmentation transition, giving rise in finite-size systems to
two regimes: bimodal magnetisation and dynamic fragmentation. Noise Targeting a
fraction of nodes preserves the transitions but introduces shattered
fragmentation with its characteristic fraction of isolated nodes and one or two
giant components. Both the lack of absorbing state for homogenous noise and the
shift in the absorbing transition to higher rewiring for targeted noise are
supported by analytical approximations.
