You should have an index table of your layout, and in your drawing method you run through this index to draw each block. Like that:
private int [][] index;
void onDraw(Canvas canvas) {
for (int i = 0; i < MAX_BLOCK_HEIGHT; i++) {
for (int j = 0; j < MAX_BLOCK_WIDTH; j++) {
// Draw block index[i][j]
}
}
}
void swapBlock(int blockX, int blockY, int relativePos) {
int tmpBlock = index[blockY][blockX];
if (relativePos == AT_LEFT) {
index[blockY][blockX] = index[blockY][blockX - 1];
index[blockY][blockX - 1] = tmpBlock;
}
// And so on...
}
And this index can be helpful all the time, not only for blit.