As someone else has mentioned, the "+" or "-" sign for your astigmatism is irrelevant, this comes from the fact there are two conventions for writing a prescription for astigmatic correction.
There will also be a 90 degree change in the axis angle when you convert from one system to the other, and if you have any sphere power in your prescription, this will also change
To convert plus cyl to minus cyl:
1. Add the cylinder power to the sphere power
2. Change the sign of the cyl from + to -
3. Add 90 degrees to the axis is less than 90 or subtract 90 if the original axis is greater than 90.
To convert minus cyl to plus cyl:
1. add the cylinder power to the sphere
2. Change the sign of the cylinder to from - to +
3. Add 90 to the axis if less than 90 or subtract if greater than 90