Intercept and Slope dummies

[Quant]

I have to estimate a model that is developed based on a difference-in-difference approach with intercept and slope dummies included. Using dummies for 2 different regimes as well as their interactions, results to a vary large model and for the sake of parsimony I decided to downsize it since the theory involved with the research assumes that only the relation between the dependent and independent variables should changes during a regime change. Therefore, I removed any intercept dummies that were not signifficant at the 10% level of signifficance. Should I do that or the presence of a slope dummy in a regression implies the mandatory presence of the respective intercept dummy (even if it is insignifficant)? Thanks in advance!