One way to make a peyote stitch tube is to weave a length of flat peyote and then zip it up. Zipping up simply means that you bring the first and last rows of beadwork together and join them.
In traditional zipping up, you use a zig-zag thread path and stitch through the protruding beads in each row.
Occasionally, however, you may need a more secure join. An example is when you make a peyote tube to serve as a sliding clasp on a bracelet. Because it's a moving clasp, the beadwork in that case is bound to experience more wear.
I use the thread path shown in the diagrams above when I need a more secure join. It resembles a basic ladder stitch. Although the ends of the beadwork are shown held apart in the diagrams, you actually want to pull the thread tight after each stitch; that pulls the edges together and creates an invisible seam.
When you complete the join, reverse direction and weave-in to end your thread, as usual.