Formula: Alternate cell values

Ok not sure how to ask this one but here I go.
I have 3 cells A1, A2, & A3. I want to leave A1 & A3 empty so that the user can input his own value without overwriting any formula there.

Now for the confusing part (to me at least), I want to put a formula in cell A2 that says if A1 has data then copy that data into A3 else if A3 has data copy the data to A1.

reason I need this is cause I have 3 sheets with the same information being entered from different sources. So I have a series of blank lines so the data can be expanded. So I want full flexibility for the user to add a source to a line and have it translated to the same line in the other sheets.
eg.: I add to store 1's first blank line "coffee filters" then I want the first blank line in the other 2 stores to say "coffee filters" But I don't want to put a formula into the blank lines.

So I figure there is a way for me to say in A2 if A1 is not empty then make A3=A1, else if A3 is not empty then make A1=A3, else do nothing.

so A1 & A3 have no formula but the formula in A2 puts values into A1 or A3.

I know I may have been a bit redundant but I hope I put it in ways so that any of you great helpers can see what I'm going for. I tend to not give enough information.
thanks for any help

I was worried that it might require vba. But I can deal with that. Well if you understood the beginning then you know what I am shooting for. As for the multiple sheets it would just be cell reference like 'store 1'A1, 'store 2'A1, & 'store 3'A1. just looking at the possibility of including multiple sheets within the same workbook.