What were the northern states which fought by the union by the following regions: new-england, mid-eastern and

Question

mid-west?

Answer 1

Pretty much what are the blue states now (plus Ohio and Indiana). Here is a directory of listings by state of all the units that fought in the US Civil War:
http://www.tarleton.edu/~kjones/unions.html

Answer 2

There's a great map at the link I supplied to Wikipedia. According to Wikipedia, the Union States were:

California
Connecticut
Delaware*
Illinois
Indiana
Iowa
Kansas
Kentucky*
Maine
Maryland*
Massachusetts
Michigan
Minnesota
Missouri*
Nevada
New Hampshire
New Jersey
New York
Ohio
Oregon
Pennsylvania
Rhode Island
Vermont
West Virginia*
Wisconsin
*denotes a Border state

Kansas, West Virginia, and Nevada joined the Union as states after the outbreak of the war.

Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont were the New England states.

Ohio, Indiana, Michigan, Illinois, Wisconsin, Iowa, Kansas, Missouri, and Minnesota were in there for the Mid-Western states.

I'm not sure of what you want when it comes to Mid-eastern. I can't find a definition of this that doesn't include the Great Lake states, many of which are part of the "Mid-west". Michigan, Delaware, New Jersey, New York, Pennsylvania, Kentucky and West Virginia would be the remaining Union States that could be classified as eastern states.

Which leaves the western states of California, Oregon, and Nevada.