Do variance of discrete white noise components cancel each other out if they have opposite signs?

Question

Suppose y^-= u + e_n - e₀ and var(e_i)=a² for i>=0.

So would var(y^-) be equal to 0 since u(mean is a constant number and has 0 variance) and var(e_n - e₀)= a²-a²=0?