Do you mean 'pop up'?

The pop-up maneuver is described here: Hacker News | The pop-up maneuver's goal is to minimize exposure to enemy fire. Imagine that y...

The concept of pop-up and defense is also here: Air defence system of Pakistan (suggestions)
in supchapter DEALING WITH LOW LEVEL AIR THREAT.

Here there are 2 terms: pop-up maneuver, and pull-up. It seems to me 'pull up' can also be used..... Pull-up phase is, as far as I understand, the ascending phase.

The word 'Потихонечку' is used several times. This should be understood as 'carefully' (like you wrote), and also in Russian can mean 'slowly, without haste', so as if to emphasize 'be attentive, careful' (because of night vision conditions).