Q:

What is the part of a bottle called where the liquid comes out?

I'm writing an academic work about pouring liquids with bottles. The different parts of the bottle are very important, because I need to distinguish between the point at the bottom, middle and top of a bottle.
But when I looked up "bottle top" it seems to be the thing that we screw on a bottle. So I tried "bottle tip" in order to not get it confused but I'm unsure if that's the best way of calling that part.  
Here's an example in which I try using it:  
The transformation from the middle of the bottle (where the end effector is grasping) to its tip equals half of the bottle height in the positive z-direction. The transformation from the glass to the bottle tip is known. 
Feel free to correct any other mistakes I might have done in those sentences. ;)

A:

This is the mouth of the bottle.

3 : something that resembles a mouth especially in affording entrance or exit: such as
[...]
c. : the opening of a container • the mouth of a bottle

from Merriam-Webster

A:

I think you are looking for rim

the outer, often curved or circular, edge of something.

Or more simply , mouth, as shown in the picture below.
Mouth: 

c : the opening of a container, the mouth of a bottle. (M-W)

A:

The part of a bottle or other vessel from which liquids or powders etc may be poured is often called a 'spout'. 

a tube-shaped opening that allows liquids to be poured out of a
  container

Spout (Cambridge)
Examples 
US patent application "a bottle cap for cutting a seal attached to a spout of a bottle to seal an opening of a bottle." 
BOTTLE CAP FOR CUTTING SEAL ATTACHED TO SPOUT OF BOTTLE
Fleming had slipped in a puddle of water which had leaked from the spout of a bottle of spring water that sat upon one of the store's shelves. 
Munford, Inc. v. Fleming (Legal case)

