When the heart is beating and everything is working the way it’s supposed to, expansion of the chest changes the pressure enough to have a small effect on systolic blood pressure (the top number).
Imagine if you were walking up an escalator and someone kept flipping the switch between up and down. Your progress up the escalator is like blood flowing through the arteries. Each step is a little push just like systole pushes blood. Each time the escalator is going up, it’s like exhaling and pushing you a little farther up. Each time the escalator is going down, it’s like inhaling and you really just stay put even though your legs are moving.