【hold up】 —

1. (of a structure, etc.) stay erect; remain in good condition:

• This building holds up well despite its age.

2. (of weather, supplies, etc.) continue; last:

• Will the water supply 【hold up】 through the summer?

3. remain in control of oneself:

• How does he 【hold up】 under such a responsibility?

【keep up】 —

1. not drown:

• The sailors managed to 【keep up】 for several hours and were eventually picked up by a lifeboat.

2. (of spirits, morale, etc.) remain high:

• His courage kept up in the face of danger.

3. = 【hold up】 2:

• Do you think this fine weather will 【keep up】 for a couple of weeks?

4. stay in touch:

• I’m afraid we haven’t kept up at all since she went abroad.

5. = 【hold up】 3:

• But for her courage, I never could have kept up through all this terrible trial.

6. not fall behind:

• If the children can 【keep up】 , we will take them with us when we hike into town.