What are key economic variables that economists use to predict a new phase of a business cycle referred to as?

They are called leading indicators.

Although there is no general consensus on the number and denomination of phases, it can be said that these are: recession, depression, recovery and boom.

There are two economic key variables used to determinate a phase which are:

GDP: Is the value of the final goods, the result of multiplying the quantity produced by the price.

Inflation: Is a macroeconomic variable that indicates the generalized increase in prices, both on goods and services, in a given period of time, usually one year.