Why when you use any filter, it results first a steepness at the beginning to a certain level? Is there any tool to avoid that? For instance, I wish after filterin my signal, the filtered signal start from a certain level, in other words, at the offset level.

In this case, I've use Butterworth, second order, freq cut-off at 0.1 Hz and sample rate at 34 ms.
If the offset is known, or can be determined before applying the filter, you can subtract the offset from the signal before applying the filter, then add the offset back after filtering.  If you don't know the offset, neither will the filter when it first starts.