I was wondering, if you take a finished Killer su Doku puzzle, and replace all the numbers like this:

1 --> 9

2 --> 8

3 --> 7

4 --> 6

5 --> 5

6 --> 4

7 --> 3

8 --> 2

9 --> 1

That is, replce every number x in the grid with (10-x), and then alter the totals of the cages accordingly (so a 14-cage that was 1-6-7 becomes a 16-cage that's 9-4-3), will you get an equivalent puzzle? Obviously, the puzzle will be valid (in the sense of having a correct solution), but will it be in essence the same puzzle, solveable by the same logical techniques at the same times in the same places? It seems to be that it would be, because the behaviour of groups of high numbers works the same way as groups of low numbers in the puzzle (like 24 has to be 9-8-7, so 6 has to be 1-2-3), but I can't work it out for sure. (Certainly it'd put paid to The Times' "Top Tip" to start with the smallest totals, seeing as in this equivalent puzzle they'd be the highest totals.)

What I'm essentially asking is this: In a regular sudoku puzzle, you can replace the numbers any way you like (swapping all the 3s and 4s, or whatever) and get the exact same puzzle to all intents and purposes. Obviously you can't do the same with Killers (or can you? Surely not) but, if you use the specific rearrangement above, does it then work?