Here’s what I noticed about the directions:
Up and down strokes make for the fastest burr formation. This is because of at least two reasons: (1) the ~3/4″ wide plate/stone is literally abrading a channel ~3/4″ wide in a specified spot on the blade; and (2) there generally tends to be more pressure applied with this motion.
This is ideal for initial profiling and chip removal, IMO, but can leave you with a “wavy” edge that has variable thicknesses along the length of the bevel. Once a burr forms on both sides of the blade, you will need to switch to a sweeping motion.
The sweeping motion blends the depths of the channels formed from the up and down strokes until they are even. This helps explain why there may not immediately be burr formation when switching from the up and down to the sweeping motion. The best way is to establish the burr with up and down strokes, then switch to a sweeping motion without changing grits. When the burr forms on the sweeping, then switch grits.
The direction of the sweep, we can argue the finer points, such as safety or the effectiveness of cutting or longevity based on the position of the scratches on the bevel…. However, the most important thing is to remove the previous grit’s scratches at each level. This can be done by alternating the sweeping position with the up and down, or by reversing the sweep stroke. I personally do up and down followed by sweeps at every level. (FWIW, I sweep from heel to tip in a downward motion).
Here’s a link to a slide show demonstrating the transition with microscope pictures. 🙂