Push-pull action is typical of the transistor half-bridge:
The power supply does not always have to be bipolar +/-.
The transistors/ mosfets do not necessarily have to be N-devices.
The output stage might have a capacitor in series, or it might be a network of components.
This simulation was done in Falstad's animated interactive simulator.
Free to download and use at:
www.falstad.com/circuit
It has the ability to export a weblink (below). It will:
(1) open the falstad.com website
(2) load my schematic into his simulator
(3) run it on your computer.
https://tinyurl.com/mtltyk8
It portrays current flow through the various paths, through all stages of the cycle.
You can change values by right-clicking on a component, and select Edit.