[gavindor]

Ag + NO3- => AgNO3 + e -

I do see what you mean, that you think the NO3- will be attracted to the silver , and that  the silver releases an electron to the battery and gives off an Ag+ cation , and that Ag+ cation reacts with the NO3-

But if that happened i'm not sure the formula would look how you put it.. 'cos your formula has neutral Ag reacting with an ion, and that looks strange to me.

[gavindor]

(I would edit the previous post to add this, but it won't let me, so i'll make this post)

Also, I don't think it's possible for both
A)an ion have an oxidation or reduction reaction at an electrode
AND
B)an electrode to get oxidised or reduced.

If the Ion  is then the electrode isn't and vice versa.

So if you're saying the NO3- loses an electron to the electrode, then the electrode is (acting) inert.  Like a graphite electrode would. And for a graphite electrode we wouldn't include that in the half equation.

So including both Silver and NO3- in an equation doesn't seem right on that basis either.

[Hunter2]

Nitrate is spectator ion. Main reaction is Ag => Ag+ + e- and vise versa. But the electrons have to be transported through the solution. The Anion does this work.