Will I still see hair removal results if I switch from Diode to YAG and then Alexandrite laser?

Female with Type III-IV skin in India where diode lasers are recommended, soon going to Dubai where Nd YAG are used and then starting grad school in Chicago, where I believe Alexandrite is popular(?). Is it a problem to change between machines? Is there a best way to go about doing this? I want to start with diode as some of my hair is finer (not too fine/virgin hair, confirmed by 2 dermats) and I believe this is the best laser for that? Nervous about deciding which laser(s) to go with+how.