mano a mano; mano mano;
man mano
As far as Italians are concerned these expressions (freely exchangeable) have only one use and meaning, the origin of which - most likely - has to do with the way in old times
people used to measure short distances by using an open hand.
You put a hand widely open beside another end moving on as you take measures. From this habit in old times
may have arisen the idea of following an event - shal we say - "step-by-step" (if you'
re measuring
long distances) ... or similarly "hand-by-hand" (if you're measuring, say, a cloth or a stick of wood, etc.).
By extension, every time an Italian wants to mean following
something very closely and at every new event uses this expression.
I mark on the wall my child's height as (mano a mano) he grows.