A nano line is a group of nano formulas which do not stack with each other.
Nano formulas in a nano line usually have similar effect types, with nanos having larger NCU costs usually having higher priority.
A nano of the same nano line and lower priority than any nano affecting the target will fail to execute on the target. Otherwise, a nano of the same nano line and higher priority than any nano affecting the target will terminate and replace lower priority nanos sharing a nano line.
Nano formulas within a nano line may also share a cooldown.
For example, if a bureaucrat executes Composite Ranged Expertise then Pistol Mastery on an adventurer, the two nano formulas have no nano line in common, so they do not interfere with each other. Both Composite Ranged Expertise and Pistol Mastery take effect, and their effects stack.
If the bureaucrat then attempts to cast Gunslinger on the adventurer, the execution fails, because Gunslinger shares a nano line with Pistol Mastery and is lower priority.
If the adventurer then executes Ballad of Smoke, Pistol Mastery terminates, because Ballad of Smoke shares a nano line with Pistol Mastery and is higher priority. The adventurer will then be affected by Composite Ranged Expertise and Ballad of Smoke.