I'm no expert by any means, but here's my take on this:
The seam down the middle is where it was blown in a mold. The mold is used for repeatability, so that consecutive bottles are all the same size and hold the same amount. That makes 2 of your 3 pieces. I'm assuming the 3rd piece is the mouth? Where the cork goes? The mark at the base of the mouth was made using a tool...don't know the name of it, but that is where the glass blower clamped the hot glass in his/her tool and pushed the glass inward, making the glass round outward at the mouth. The cork expands into this opening and helps to keep the bottle sealed.