Rewriting List of Matrix Equation in Terms of Individual Equations?

Question

I have a list of matrix equations

M1={{a1,b1},{c1,d1}};
A1={{x1,y1},{z1,w1}};
M2={{a2,b2},{c2,d2}};
A2={{x2,y2},{z2,w2}};
sys={M1==A1,M2==A2};

which I would like to rewrite as

{a1==x1,b1==y1,c1==z1,d1==w1,a2==x2,b2==y2,c2==z2,d2==w2}.

How can this be done?