A breath begins with the inbreath. The transition from inbreath to outbreath is smooth, like reaching the top of a rounded hill and then continuing on going down. There is no particular action involved, one movement simply merges into the other. The transition from outbreath to inbreath is more like a cusp, a distinct change of direction, you have reached the basement and could almost stay there but for a decision to go up again. Either way, however, there is a moment of stillness, and because all thought is tied to the action of breathing, thought stops, or the sense of time, which is itself only a thought. That's why these moments of stillness seem to expand indefinitely. The quality of this expansion persists into the next breath. Focus on that moment can be cultivated, mostly, even if you are attending closely to it you miss it because the experiencing is replaced by the idea of the experience, the mind so ready to anticipate, to overshoot.