Before revision:  We introduce a " Markov chains of Markov chains " model such that with probably (1-\omega) \in[0,1]  random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) interlayer Markov chains .
After revision:  We introduce a " Markov chains of Markov chains " model such that with probably (1-\omega) \in[0,1] 0,1 random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) interlayer Markov chains .