Yes, your maternal and paternal crossover maps are independent. Each set of your chromosomes was independently created in each parent before you were conceived – there could be no mixing between your parents. And, yes, on one maternal chromosome, segments from your two maternal grandparents are adjacent and alternating. NB: An entire chromosome could be from only one grandparent – one large segment. In fact there is a high probability that this happened in at least one of your shorter chromosomes (17 to 22).