  Cascading failures may lead to dramatic collapse in interdependent networks,
where the breakdown takes place as a discontinuity of the order parameter. In
the cascading failure (CF) model with healing there is a control parameter
which at some value suppresses the discontinuity of the order parameter.
However, up to this value of the healing parameter the breakdown is a hybrid
transition, meaning that, besides this first order character, the transition
shows scaling too. In this paper we investigate the question of universality
related to the scaling behavior. Recently we showed that the hybrid phase
transition in the original CF model has two sets of exponents describing
respectively the order parameter and the cascade statistics, which are
connected by a scaling law. In the CF model with healing we measure these
exponents as a function of the healing parameter. We find two universality
classes: In the wide range below the critical healing value the exponents agree
with those of the original model, while above this value the model displays
trivial scaling meaning that fluctuations follow the central limit theorem.
