Hidden Markov Model between groups

I would like to use a HMM in my research project, but I have some questions accordingly. I have data from 2 groups (younger and older) and I want to run a HMM to identify sleep stages. I could run the HMM on my complete data and could compare the phase occurence and phase transitions between the groups. But what can I do to compare the transition probability matrix between the groups? In the python package hmmlearn I can only look at the transition matrix of my full dataset, but not for the individual groups. But If I train the HMM seperately, the identified states would not be comparable, right? Is there a way to calculate the transition matrix for each group/individual without loosing the interpretability of the hidden states (one hidden state has the same label in al groups) ?
Thanks for your help.