This talk is about connections between irreducible and absorbing Markov chains. One of those connections is using Sigmund duality theory. In the talk, we will describe a more direct way of associating the two classes of processes, allowing to evaluate important quantities defined in one of the chains by calculating on the other one. Using this connection, we will focus on a specific application of previous result, the derivation of relations in the absorbing process similar to equilibrium through cuts operating on the corresponding irreducible chain. These relations provide equilibrium equations allowing to obtain more easily quantities associated with the process in equilibrium. In the absorbing case, the corresponding relations connect mean sojourn times in the transient states until absorption. We will illustrate them with simple examples using both finite and infinite absorbing processes.