Pressure equalization apparatus and associated systems and methods

A method of installing a well tool in a well, the method comprising:

• attaching a mandrel to the well tool;
• then lowering the well tool at least partially into the well suspended from the mandrel;
• and
• then securing a pressure equalization apparatus to the mandrel, a flowpath of the apparatus being connected to a chamber of the well tool containing an assembly, wherein the flowpath has first and second opposite ends, the first end being connected to the chamber, the second end being connected to a source of a second fluid, the flowpath extending in alternating opposite directions between the first and second ends through multiple separate bores and wherein the multiple bores include at least first and second bores, and wherein at least one end closure having a plurality of passages formed therein connect an end of the first bore to an adjacent end of the second bore, wherein the flowpath prevents migration of fluid through the flowpath while permitting pressure communication through the flowpath.