Why is a net flow of positive charge in one direction equivalent to a net flow of negative charge in the opposite direction? If I understand correctly, conventional current was defined with reference to positive charges because it was found that a negative charge flowing in one direction is actually equivalent to the same amount of positive charge going in the other direction.
Is there any basis for this equivalence?
 A: It’s an historical question. It is my understanding that the convention for current flow being that of positive charge occurred before electrical current was really understood. So in electrical engineering it’s the convention that stuck. Physicists don’t care for it since we now know that most current is the flow of negative charge, electrons (semi conductor currently being one exception). Bottom line: It doesn’t matter as long as we’re consistent.
UPDATE:
Read that Ben Franklin in static electricity  experiments knew there were two types of charge depending on what materials you rubbed together. He thought of current as a fluid which if built up too much , became too “positive”, it would discharge causing a spark.  
If this true, then it has nothing to with positive charge going in one direction being equivalent to negative charge going in the opposite direction.
Hope this helps 
P.s the above is from “The Direction Assigned to Electric Currents” NASA website Here is the link.https://www-spof.gsfc.nasa.gov/Education/woppos.html
A: 
is there any basis for this equivalence ?

Consider an initially electrically neutral region (equal number of unit positive and negative electric charge) and consider the flow of electric charge through a closed surface enclosing the volume.
Stipulate there is a net outward flow of positive (negative) charge through the surface and see that the region becomes progressively more negatively (positively) charged.
Now, stipulate that there is a net inward flow of negative (positive) charge through the surface and see that the region become progressively more negatively (positively) charged.
That is, the region is becoming progressively more negatively (positively) charged in either case.
A: It's appropriate to remark that equivalence is not always true. I wish to remind you of Hall effect. Shortly said, there is a difference when a conductor is placed in a magnetic field. A weak transverse (wrt current and field) potential difference is observed, and its direction depends on whether charge carriers are positive or negative.
Of course that effect was discovered much later than the sign convention had been established. Initially it was a mistery: some conductors exhibited a sign of Hall effect opposite to the vast majority. Explanation had to wait quantum mechanics and the band theory of solid state.
