It is hard to find any reference which contains a proof of the following statement: slope stability is an open condition in a flat family. 
There is one I have found, '65 paper of Narasimhan and Seshadri. Is this the unique reference which proves the statement?
There are some references which prove the openness of Gieseker stability, but what I want is about slope stability.
I will be appreciate if one introduces a reference other than Narasimhan and Seshadri...



reference required: slope stability is an open condition
In the second edition of "The Geometry of Moduli Spaces of Sheaves" by Huybrechts and Lehn, the arguments in Proposition 2.3.1 which imply (for instance) that Gieseker-semistability is an open condition in families also imply the same for $\mu$-stability (this is pointed out just after Definition 3.A.1 on p. 82).


