As the owner-builder you will be the holder of the “master permit”. All other trades that require an inspection will be required to pull permits under their name and your master permit.
At your local building & permits office (and their website) you will be able to find their specific application process and documents. You do not need to be classified as a pool company to obtain the permits when applying as the owner-builder.
Once you have finalized your subcontractor selections you will then need to send out your master-permit information so any who need to obtain subsequent permits may do so.
Any of the subs that you hire where the stage of construction is cause for municipal inspections will have paid for and obtained their “trade-permit” prior to beginning their scope of the work.
Who calls for the inspections?
As per each municipality specific instructions and schedule of required inspections it will be a combination of you and your subcontractors.