You may be eligible for a dismissal under penal code section 1203.4 of your crimes.
There are some factors that must first be determined before anyone can state whether you qualify.
If you'd like more information or have any questions and would like a free consultation, please feel free to call me.
There isn't much you can do to prevent them from showing up on a background check, unless you were a minor at the time of the offense and these were juvenile court matters. You may be eligible for relief under Penal Code Section 1203.4 if you are not now on probation or parole and are not charged with any offense. You should consult with an attorney to review the facts of your conviction(s) and determine if you qualify for relief.
No attorney-client relationship is established between this lawyer and the originator of the question. This answer is provided for informational purposes only and is provided purely to assist the questioner in determining whether to consult with an attorney to obtain legal advice specific to their matter.
There is nothing that you can do to ever get the convictions off of your record, but there may be a couple things that you can do to be able to legally and truthfully answer that you have never been convicted of a felony and even that you have never been convicted of a crime. This will depend on what the offenses you were convicted of and what the sentence you served was, so more information is necessary in order to give you a more specific answer.
The other attorney's wrote a pretty straightforward answer. The arrest cannot be removed, because you entered into a plea or were convicted of the offense. PC Section 1203.4 is the only way to expunge the plea or conviction. While everything remains part of the public record, it is unlawful for an employer to deny you employment for this alone. After you get a 1203.4 (a) as you were on some form of probation no A if you were not) the guilty plea is withdrawn and the complaint is set aside. Even a Governor's pardon would still show as part of your criminal history. A 1203.4 essentially is a rehabilitation step. You still have to disclose to any peace office position or if you work or are part of the lottery system. Good luck!