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If you received and accepted an offer it is likely you agreed to start the new job on a certain date typically two weeks. Give your two week notice and leave. If your present employer wants you to stay they are asking you to probably screw up the new job. That has a value, a big one. If current employer wants you to stay they can make a counter. I would suggest that the value of screwing up the new employment is large. ALSO if they offer to promote you or give you a raise, you have to wonder why they didn't already do it. Make a careful decision no matter what and get your value
If you've already informed your current employer that you've found a new job, it's up to them whether you remain or leave. Many IT Companies would probably want you gone ASAP, as there's always a chance you could plant 'sleepers' in a Software project, timed to destroy everything, once they've left. However, in another situation, you may be a key worker & leaving the company high & dry isn't a good thing to do at all... especially if you're wanting a Reference from them, or mention it on your CV/Resume, should you change jobs again. Also, you may want to return to the old job, if things don't work out at the new place. If you've just 'up-sticks' & left, it's extremely doubtful you'd ever get back in!
Ideally, it's recommended you give at least 2 weeks notice before leaving a job; though the sooner the better. That way they can make appropriate arrangements in such circumstances as need be. You CAN leave asap, though that's a good way to burn bridges. Especially if you ever want to work at that job again, or you need someone there as a reference. So I wouldn't recommend that option if you can avoid doing so, or you're sure it will cause no harm to you in the long run.
I meant working your notice period By ASAP. Tieing up the project would take longer than the notice period.
You should at least give a notice period.
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