The electronic transport properties and the magnetic susceptibility were measured in detail in $YBaCo_2O_{5.45}$. Close to the so-called metal-insulator transition, strong effects of resistance relaxation, a clear thermal hysteresis and a sudden increase of the resistance noise are observed. This is likely due to the first order character of the transition and to the underlying phases coexistence. Despite these out of equilibrium features, a positive and linear magneto-resistance is also observed, possibly linked to the heterogeneity of the state. From a magnetic point of view, the paramagnetic to ordered magnetic state transition is observed using non linear susceptibilty. This transition shows the characteristics of a continuous transition, and time dependent effects can be linked with the dynamics of magnetic domains in presence of disorder. Thus, when focusing on the order of the transitions, the electronic one and the magnetic one can not be directly associated.
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